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Zweizig10aaThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration 1 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany 2 LIGO Hanford Observatory, Richland, WA 99352, USA 3 Dipartimento di Farmacia, Università di Salerno, I-84084 Fisciano, Salerno, Italy 4 INFN, Sezione di Napoli, I-80126 Napoli, Italy 5 University of Warwick, Coventry CV 4 7AL, UK 6 The Pennsylvania State University, University Park, PA 16802, USA 7Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany 8 Leibniz Universität Hannover, D-30167 Hannover, Germany 9 University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA 10 LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA 11 Louisiana State University, Baton Rouge, LA 70803, USA 12 Tata Institute of Fundamental Research, Mumbai 400005, India 13 Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium 14 Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India 15 Queen Mary University of London, London E1 4NS, UK 16 Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea 17 Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil 18 SUPA, University of the West of Scotland, Paisley PA1 2BE, UK 19 Università di Roma Tor Vergata, I-00133 Roma, Italy 20 INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy 21 Universiteit Antwerpen, 2000 Antwerpen, Belgium 22 International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India 23 University College Dublin, Belfield, Dublin 4, Ireland 24 Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan 25 Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan 26 Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, D-07743 Jena, Germany 27 INFN Sezione di Torino, I-10125 Torino, Italy 28 SUPA, University of Glasgow, Glasgow G12 8QQ, UK 29 OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia 30 Univ. 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https://orcid.org/0000-0002-7453-6372 https://orcid.org/0000-0002-1521-3397 42 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain 43 Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy 44 University of Florida, Gainesville, FL 32611, USA 45 Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, I-33100 Udine, Italy 46 INFN, Sezione di Trieste, I-34127 Trieste, Italy 47 Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Monterrey 64849, Mexico 48 Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Artemis, F-06304 Nice, France 49 Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan 50 INFN, Sezione di Perugia, I-06123 Perugia, Italy 51 Università di Camerino, I-62032 Camerino, Italy 52 University of Washington, Seattle, WA 98195, USA 53 Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan 54 California State University Fullerton, Fullerton, CA 92831, USA 55 Villanova University, Villanova, PA 19085, USA 56 INFN, Sezione di Genova, I-16146 Genova, Italy 57 Dipartimento di Fisica, Università degli Studi di Genova, I-16146 Genova, Italy 58 SUPA, University of Strathclyde, Glasgow G1 1XQ, UK 59 European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy 60 Georgia Institute of Technology, Atlanta, GA 30332, USA 61 Royal Holloway, University of London, London TW20 0EX, UK 62 Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan 63 Università degli Studi di Urbino “Carlo Bo,” I-61029 Urbino, Italy 64 INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy 65 LIGO Livingston Observatory, Livingston, LA 70754, USA 66 INFN, Sezione di Roma, I-00185 Roma, Italy 67 Università di Roma “La Sapienza”, I-00185 Roma, Italy 68 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France 69 Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA 70 Dipartimento di Fisica “E.R. Caianiello,” Università di Salerno, I-84084 Fisciano, Salerno, Italy 71 Université Paris Cité, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France 72 King’s College London, University of London, London WC2R 2LS, UK 73 Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea 74 Université libre de Bruxelles, 1050 Bruxelles, Belgium 75 International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan 76 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands 77 University of Portsmouth, Portsmouth, PO1 3FX, UK 78 University of Oregon, Eugene, OR 97403, USA 79 Syracuse University, Syracuse, NY 13244, USA 80 Northwestern University, Evanston, IL 60208, USA 81 Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), c. Martí i Franqués, 1, 08028 Barcelona, Spain 82 Dipartimento di Medicina, Chirurgia e Odontoiatria “Scuola Medica Salernitana,” Università di Salerno, I-84081 Baronissi, Salerno, Italy 83 HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary 84 Concordia University Wisconsin, Mequon, WI 53097, USA 85 Universität Hamburg, D-22761 Hamburg, Germany 86 Stanford University, Stanford, CA 94305, USA 87 Università di Pisa, I-56127 Pisa, Italy 88 INFN, Sezione di Pisa, I-56127 Pisa, Italy 89 Università di Perugia, I-06123 Perugia, Italy 90 University of Michigan, Ann Arbor, MI 48109, USA 91 Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy 92 INFN, Sezione di Padova, I-35131 Padova, Italy 93 Institute for Plasma Research, Bhat, Gandhinagar 382428, India 94 Universiteit Gent, B-9000 Gent, Belgium 95 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland 96 University of Minnesota, Minneapolis, MN 55455, USA 97 Université Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France 98 IAC3–IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain 99 Università di Siena, I-53100 Siena, Italy 100 RRCAT, Indore, Madhya Pradesh 452013, India 101 Kenyon College, Gambier, OH 43022, USA 102 Missouri University of Science and Technology, Rolla, MO 65409, USA 103 Colorado State University, Fort Collins, CO 80523, USA 104 Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands 105 Lomonosov Moscow State University, Moscow 119991, Russia 106 Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium 107 Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy 108 INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy 109 Rochester Institute of Technology, Rochester, NY 14623, USA 110 Bar-Ilan University, Ramat Gan, 5290002, Israel 111 University of British Columbia, Vancouver, BC V6T 1Z4, Canada 112 INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy 113 OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia 114 Centre national de la recherche scientifique, 75016 Paris, France 115 Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France 116 University of Birmingham, Birmingham B15 2TT, UK 117Washington State University, Pullman, WA 99164, USA 6 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. 118 INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy 119 Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, F-75005 Paris, France 120 Christopher Newport University, Newport News, VA 23606, USA 121 OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia 122 Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland 123 University of Maryland, College Park, MD 20742, USA 124 Università degli Studi di Milano-Bicocca, I-20126 Milano, Italy 125 INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy 126 L2IT, Laboratoire des 2 Infinis - Toulouse, Université de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France 127 Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France 128 IGFAE, Universidade de Santiago de Compostela, 15782, Spain 129 University of Chicago, Chicago, IL 60637, USA 130 University of Arizona, Tucson, AZ 85721, USA 131 University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA 132 INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy 133 Niels Bohr Institute, Copenhagen University, 2100 København, Denmark 134 Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy 135 Departamento de Astronomía y Astrofísica, Universitat de València, E-46100 Burjassot, València, Spain 136 Observatori Astronòmic, Universitat de València, E-46980 Paterna, València, Spain 137 Niels Bohr Institute, University of Copenhagen, 2100 Kóbenhavn, Denmark 138 Department of Physics, National Cheng Kung University, No. 1, University Road, Tainan City 701, Taiwan 139 National Tsing Hua University, Hsinchu City 30013, Taiwan 140 National Central University, Taoyuan City 320317, Taiwan 141 OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia 142 Vanderbilt University, Nashville, TN 37235, USA 143 Department of Electrophysics, National Yang Ming Chiao Tung University, 101 University Street, Hsinchu, Taiwan 144 Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan 145 University of Texas, Austin, TX 78712, USA 146 CaRT, California Institute of Technology, Pasadena, CA 91125, USA 147 Cornell University, Ithaca, NY 14850, USA 148 Northeastern University, Boston, MA 02115, USA 149 OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia 150 Dipartimento di Ingegneria Industriale (DIIN), Università di Salerno, I-84084 Fisciano, Salerno, Italy 151 INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy 152 OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia 153 University of Rhode Island, Kingston, RI 02881, USA 154 INFN Cagliari, Physics Department, Università degli Studi di Cagliari, Cagliari 09042, Italy 155 Université Libre de Bruxelles, Brussels 1050, Belgium 156 INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy 157 Departamento de Matemáticas, Universitat de València, E-46100 Burjassot, València, Spain 158 Montana State University, Bozeman, MT 59717, USA 159 Johns Hopkins University, Baltimore, MD 21218, USA 160 The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA 161 Université de Liège, B-4000 Liège, Belgium 162 DIFA- Alma Mater Studiorum Università di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy 163 Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2, Bologna, Italy 164 University of Manitoba, Winnipeg, MB R3T 2N2, Canada 165 INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy 166 Chennai Mathematical Institute, Chennai 603103, India 167 Università degli Studi di Sassari, I-07100 Sassari, Italy 168 Université de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France 169 Laboratoire de Physique Corpusculaire Caen, 6 boulevard du maréchal Juin, F-14050 Caen, France 170 Université Claude Bernard Lyon 1, CNRS, Laboratoire des Matériaux Avancés (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France 171 Università di Firenze, Sesto Fiorentino I-50019, Italy 172 Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy 173 INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy 174 University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy 175 Marquette University, Milwaukee, WI 53233, USA 176 Perimeter Institute, Waterloo, ON N2L 2Y5, Canada 177 Corps des Mines, Mines Paris, Université PSL, 60 Bd Saint-Michel, 75272 Paris, France 178 Indian Institute of Technology Madras, Chennai 600036, India 179 Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan 180 National Center for Nuclear Research, 05-400 Świerk-Otwock, Poland 181 Institut d’Astrophysique de Paris, Sorbonne Université, CNRS, UMR 7095, 75014 Paris, France 182 Vrije Universiteit Brussel, 1050 Brussel, Belgium 183 Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan 184 Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada 185 University of Cambridge, Cambridge CB2 1TN, UK 186 Stony Brook University, Stony Brook, NY 11794, USA 187 Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA 188 Montclair State University, Montclair, NJ 07043, USA 189 Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy 190 HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary 191 Centro de Física das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal 192 Centre de Physique des Particules de Marseille, 163, avenue de Luminy, 13288 Marseille cedex 09, France 193 CNR-SPIN, I-84084 Fisciano, Salerno, Italy 7 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. 194 Scuola di Ingegneria, Università della Basilicata, I-85100 Potenza, Italy 195 Western Washington University, Bellingham, WA 98225, USA 196 Barry University, Miami Shores, FL 33168, USA 197 Centro de Astrofísica e Gravitação, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa - UL, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal 198 Eötvös University, Budapest 1117, Hungary 199 Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan 200 Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan 201 Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Lagrange, F-06304 Nice, France 202 California State University, Los Angeles, Los Angeles, CA 90032, USA 203 Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain 204 University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland 205 Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, F-72085 Le Mans, France 206 University of Szeged, Dóm tér 9, Szeged 6720, Hungary 207 Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India 208 School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, People’s Republic of China 209 University of California, Riverside, Riverside, CA 92521, USA 210 University of Nottingham NG7 2RD, UK 211 Ariel University, Ramat HaGolan St 65, Ari’el, Israel 212 University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Pacific, Bejing 100049, People’s Republic of China 213 The University of Mississippi, University, MS 38677, USA 214 Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan 215 Science and Technology Institute, Universities Space Research Association, Huntsville, AL 35805, USA 216 Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, People’s Republic of China 217 The Chinese University of Hong Kong, Shatin, NT, Hong Kong 218 American University, Washington, DC 20016, USA 219 University of Nevada, Las Vegas, Las Vegas, NV 89154, USA 220 Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan 221 University of California, Berkeley, CA 94720, USA 222 University of Lancaster, Lancaster LA1 4YW, UK 223 College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan 224 Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan 225 Department of Physics, Tamkang University, No. 151, Yingzhuan Road, Danshui District, New Taipei City 25137, Taiwan 226 Rutherford Appleton Laboratory, Didcot OX11 0DE, UK 227 Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea 228 Scuola Normale Superiore, I-56126 Pisa, Italy 229 Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, People’s Republic of China 230 Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan 231 Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan 232 Directorate of Construction, Services & Estate Management, Mumbai 400094, India 233 Faculty of Physics, University of Białystok, 15-245 Białystok, Poland 234 University of Southampton, Southampton SO17 1BJ, UK 235 Sungkyunkwan University, Seoul 03063, Republic of Korea 236 Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea 237 Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan 238 Chung-Ang University, Seoul 06974, Republic of Korea 239 University of Washington Bothell, Bothell, WA 98011, USA 240 Aix Marseille Université, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France 241 Laboratoire de Physique et de Chimie de l’Environnement, Université Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso 242 Ewha Womans University, Seoul 03760, Republic of Korea 243 Seoul National University, Seoul 08826, Republic of Korea 244 Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea 245 Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan 246 Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan 247 Bard College, Annandale-On-Hudson, NY 12504, USA 248 Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland 249 Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland 250 Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy 251 Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy 252 Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan 253 Université de Montréal/Polytechnique, Montreal, QC H3T 1J4, Canada 254 Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India 255 Texas Tech University, Lubbock, TX 79409, USA 256 Università degli Studi di Cagliari, Via Università 40, 09124 Cagliari, Italy 257 Inje University Gimhae, South Gyeongsang 50834, Republic of Korea 258 Technology Center for Astronomy and Space Science, Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea 259 NAVIER, École des Ponts, Univ Gustave Eiffel, CNRS. Marne-la-Vallée, France 260 National Center for High-Performance Computing, National Applied Research Laboratories, No. 7, R&D 6th Road, Hsinchu Science Park, Hsinchu City 30076, Taiwan 261 NAS. Marshall Space Flight Center, Huntsville, AL 35811, USA 262 Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany 263 School of Physics Science and Engineering, Tongji University, Shanghai 200092, People’s Republic of China 264 Institut d’Estudis Espacials de Catalunya, c. Gran Capità, 2-4, 08034 Barcelona, Spain 265 Columbia University, New York, NY 10027, USA 8 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. 266 Institucio Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys, 23, 08010 Barcelona, Spain 267 Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224- 8551, Japan 268 Tsinghua University, Beijing 100084, People’S Republic of China 269 Institute for Photon Science and Technology, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan 270 School of Physical & Chemical Sciences, University of Canterbury, Private Bag 4800, Christchurch 8041, New Zealand 271 GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands 272 Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France 273 Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan 274 Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA 275 Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, To Huu street Yen Nghia Ward, Ha Dong District, Hanoi, Vietnam 276 University of Stavanger, 4021 Stavanger, Norway 277 Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 278 Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 903- 0213, Japan 279 Observatoire Astronomique de Strasbourg, 11 Rue de l’Université, 67000 Strasbourg, France 280 Observatoire de Paris, 75014 Paris, France 281 Laboratoire Univers et Théories, Observatoire de Paris, 92190 Meudon, France 282 National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea 283 Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan 284 Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122, Japan 285 University of Maryland, Baltimore County, Baltimore, MD 21250, USA 286 CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India 287 Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy 288 Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece 289 Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea 290 Department of Physics, University of Guadalajara, Av. Revolucion 1500, Colonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico 291 Hobart and William Smith Colleges, Geneva, NY 14456, USA 292 Dipartimento di Ingegneria, Università del Sannio, I-82100 Benevento, Italy 293 Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi,” I-00184 Roma, Italy 294 Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Università degli Studi Roma Tre, I-00146 Roma, Italy 295 Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Université, 4 rue Alfred Kastler BP 20722 44307 Nantes CÉDEX 03, France 296 Universidad de Antioquia, Medellín, Colombia 297 Departamento de Física - ETSIDI, Universidad Politécnica de Madrid, 28012 Madrid, Spain 298 Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan 299 Dipartimento di Fisica e Scienze della Terra, Università Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy 300 Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan 301 Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India 302 Laboratoire MSME, Cité Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France 303 University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan 304 Institute for Quantum Studies, Chapman University, 1 University Drive, Orange, CA 92866, USA 305 Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan 306 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 307 iTHEMS (Interdisciplinary Theoretical and Mathematical Sciences Program), RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan 308 Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, I-34136, Trieste TS, Italy 309 Laboratoire de Physique de l’École Normale Supérieure, ENS, (CNRS, Université PSL, Sorbonne Université, Université Paris Cité), F-75005 Paris, France 310 Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany 311 INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy 312 Universidade Estadual Paulista, 01140-070 São Paulo, Brazil 313 Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland 314 Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan 315 Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan 316 Carleton College, Northfield, MN 55057, USA 317 University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy 318 National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan 319 Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan 320 Texas A&M University, College Station, TX 77843, USA 321 Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands 322 The University of Utah, Salt Lake City, UT 84112, USA 323 Kavli Institute for the Physics and Mathematics of the Universe, WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan 324 Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, People’s Republic of China Received 2025 August 26; revised 2025 September 23; accepted 2025 September 26; published 2025 December 9 Abstract The Gravitational-Wave Transient Catalog (GWTC) is a collection of short-duration (transient) gravitational- wave signals identified by the LIGO–Virgo–KAGRA Collaboration in gravitational-wave data produced by the 325 Deceased, 2024 September. 326 Deceased, 2025 August. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 9 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. https://creativecommons.org/licenses/by/4.0/ eponymous detectors. The catalog provides information about the identified candidates, such as the arrival time and amplitude of the signal and properties of the signal’s source as inferred from the observational data. GWTC is the data release of this dataset, and version 4.0 extends the catalog to include observations made during the first part of the fourth LIGO–Virgo–KAGRA observing run up until 2024 January 31. This Letter marks an introduction to a collection of articles related to this version of the catalog, GWTC-4.0. The collection of articles accompanying the catalog provides documentation of the methods used to analyze the data, summaries of the catalog of events, observational measurements drawn from the population, and detailed discussions of selected candidates. Unified Astronomy Thesaurus concepts: Gravitational wave astronomy (675); Gravitational wave detectors (676); Gravitational wave sources (677); Stellar mass black holes (1611); Neutron stars (1108) 1. Overview The Laser Interferometer Gravitational-Wave Observatory (LIGO; J. Aasi et al. 2015a) and the Virgo (F. Acernese et al. 2015) and KAGRA (T. Akutsu et al. 2021) observatories form an international network of ground-based gravitational-wave (GW) detectors. This Letter is an introduction to the collection of articles describing the contents of the LIGO–Virgo– KAGRA Collaboration (LVK) Gravitational-Wave Transient Catalog (GWTC) version 4.0, hereafter GWTC-4.0, along with reviews of the methods used in various aspects in the construction of this catalog, astrophysical and cosmological implications of the observations, and tests of general relativity (GR) that are performed on the observed transients. This Letter provides details on the network of GW detectors, the observing runs, observatory evolution, and a review of the transient signals that have been identified. In addition, we describe conventions and notations that are used throughout the collection of articles accompanying the catalog. 1.1. The GWTC Sources and Science Transient GW signals may be produced by a variety of astrophysical sources, including compact binary coalescences (CBCs) of compact objects such as black holes (BHs) and neutron stars (NSs), core-collapse supernovae, and other explosive phenomena (B. P. Abbott et al. 2020a). The first observed GW transient, GW150914, was a binary BH (BBH) coalescence (B. P. Abbott et al. 2016a), and we have since observed a binary NS (BNS) coalescence (B. P. Abbott et al. 2017a) that had associated electromagnetic counterparts (B. P. Abbott et al. 2017b) and NS–BH binary (NSBH) coalescences (R. Abbott et al. 2020d). This GWTC-4.0 collection of articles describes the GW transient candidates observed by the LVK from the observing run (O1) through the end of the fourth observing run (O4a) and the astrophysical implications of these observations. The article collection includes the following: 1. “GWTC-4.0: Methods for Identifying and Characterizing Gravitational-wave Transients” (A. G. Abac et al. 2025a) reviews the procedures used to go from the calibrated output of the detectors to a list of transient candidates that includes measurements of the statistical significance and inferences on each of the corresponding astrophy- sical sources. 2. “GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth LIGO–Virgo–KAGRA Observing Run” (A. G. Abac et al. 2025b) describes the primary observational results contained in GWTC-4.0: the significant GW transient candidates observed through the end of the O4a observing run and the inferred source parameters under the hypothesis that these transients arise from GWs emitted by CBCs (Section 5.2). 3. “GWTC-4.0: Population Properties of Merging Compact Binaries” (A. G. Abac et al. 2025c) describes the underlying population of CBCs inferred using GWTC-4.0 data and related astrophysical implications. 4. “GWTC-4.0: Tests of General Relativity I—Overview and General Tests” (A. G. Abac et al. 2025d) presents an overview of the methods and tests of GR performed on the subset of signals suitable for such tests and focuses on the general and consistency tests. 5. “GWTC-4.0: Tests of General Relativity II—Parameter- ized Tests” (A. G. Abac et al. 2025e) describes the parameterized tests of GR performed on the signals. 6. “GWTC-4.0: Tests of General Relativity III—Tests of the Remnant” (A. G. Abac et al. 2025f) describes the tests of the coalescence remnants. 7. “GWTC-4.0: Constraints on the Cosmic Expansion Rate and Modified Gravitational-wave Propagation” (A. G. Abac et al. 2025g) describes the methods used to determine the Hubble constant and related parameters, including parameterized deviations from GR on cosmo- logical scales, using GWTC-4.0 candidates. 8. “GWTC-4.0: Searches for Gravitational Wave Lensing Signatures” (A. G. Abac et al. 2025h) describes the searches for lensed GW signals in the geometric and wave optics regime in the GWTC-4.0 dataset. It also sets constraints on the merger rate at high redshift and the relative rate of strongly lensed signals compared to unlensed ones. 9. “Open Data from LIGO, Virgo, and KAGRA through the First Part of the Fourth Observing Run” (A. G. Abac et al. 2025i) describes the publicly accessible data and other science products that can be freely accessed through the Gravitational Wave Open Science Center (GWOSC). These data sets include the raw GW strain time series, details of the calibration and cleaning process, efforts to remove instrumental noise artifacts, and details of the online GWTC-4.0. 10. “GW230814: Investigation of a Loud Gravitational-wave Signal Observed with a Single Detector” (A. G. Abac et al. 2025j) describes the analysis of the loudest event in the GWTC-4.0 catalog, GW230814_230901, which was detected on 2023 August 14. This event is notable for its high signal-to-noise ratio (SNR) and its potential implications for our understanding of GW signals and GR. 11. “GW231123: a Binary Black Hole Merger with Total Mass 190–265M⊙ ” (A. G. Abac et al. 2025k) describes 10 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. http://astrothesaurus.org/uat/675 http://astrothesaurus.org/uat/676 http://astrothesaurus.org/uat/677 http://astrothesaurus.org/uat/1611 http://astrothesaurus.org/uat/1108 the analysis of the candidate GW231123_135430, detected on 2023 November 23. The candidate’s source is exceptional, having the highest inferred total mass of any high-confidence BBH observations to date. To reference the whole GWTC-4.0 collection, we encourage citing this introductory Letter. 1.2. The Electronic Catalog: GWTC A. G. Abac et al. (2025i) document the released open data, including the GWTC dataset. The catalog contains candidates (sometimes called events) identified in observational data that are deemed likely to be caused by GW signals, as well as triggers corresponding to times selected by searches of the data for GW transient signals that potentially contain an identifiable signal but with lower confidence of being caused by a GW. 1.2.1. The Catalog Naming Convention The LVK GWTC is a cumulative dataset containing data on all transient candidates reported by the LVK. Released versions of the catalog have major and minor numbers in the format GWTC major minor. .< > < > The major number is determined by the span of time containing all candidates in the catalog as described below. Prior to GWTC-4.0, the minor number was routinely omitted when describing a catalog version when that minor number was 0, so GWTC-1.0, GWTC-2.0, and GWTC-3.0 were referred to as GWTC-1, GWTC-2, and GWTC-3 in the articles that described those catalog versions. In this Letter, and in the future, we will include the .0 when referring to those catalog versions. We also say that GWTC– can refer to GWTC–. for any minor version having that major version number. Each catalog version is a superset of the previous one (apart from retracted candidates), so that, for example, GWTC-3.0 (R. Abbott et al. 2023) contains all the candidates in GWTC- 2.1 (R. Abbott et al. 2024). Since GWTC-2.1 provided a deeper list of candidates observed over the same period as GWTC-2.0 (R. Abbott et al. 2021b), the minor version numbers of these two releases differ while their major version numbers remain the same. In general: 1. The major number is incremented when the span of time over which observational data were searched for transients is increased. 2. The minor version resets to 0 when the major version number is increased. 3. The minor version is incremented when there is a change in the data describing the transients (additional data, modified data, or removed data) contained in the catalog within the current time span covered. The time span covering the transient candidates in the catalog indicated by the major number is as follows: GWTC-1: Contains candidates occurring in data taken before 2018 October 1 00:00:00. The GWTC- 1.0 dataset is described in B. P. Abbott et al. (2019a). GWTC-2: Contains candidates occurring in data taken before 2019 October 1 15:00:00. The GWTC-2.0 dataset is described in R. Abbott et al. (2021b) and the GWTC-2.1 dataset in R. Abbott et al. (2024). GWTC-3: Contains candidates occurring in data taken before 2020 May 1 00:00:00. The GWTC-3.0 dataset is described in R. Abbott et al. (2023). GWTC-4: Contains candidates occurring in data taken before 2024 January 31 00:00:00. The GWTC- 4.0 dataset is described in A. G. Abac et al. (2025b). In addition to GWTC, other catalogs of GW transients include the Open Gravitational-wave Catalog (OGC), the most recent version 4-OGC contains observations from 2015 to 2020 (A. H. Nitz et al. 2023), as well as catalogs of candidate signals identified by the IAS pipeline (T. Venumadhav et al. 2019; S. Olsen et al. 2022; D. Wadekar et al. 2024; M. H.-Y. Cheung et al. 2025). A. G. Abac et al. (2025i) provide details on the GWOSC event portal,327 a database of published GW transient events, including Community Cata- logs (J. Kanner et al. 2025) containing catalog results from communities outside of the LVK. 1.2.2. Candidate Naming Conventions The naming of our GW candidates follows the format GW YY MM DD hh mm ss_ ,< > < > < > < > < > < > encoding the date and Coordinated Universal Time (UTC) of the signal. For example, GW200105_162426 was the transient observed on 2020 January 5 at 16:24:26 UTC. For transient signals spanning multiple-second intervals, the time assigned to a signal is an estimate of the time of peak GW amplitude. GW candidates reported prior to the release of GWTC-2.0 were designated by the abbreviated form GW YY MM DD ,< > < > < > including candidates first appearing in GWTC-1.0 (B. P. Abbott et al. 2019a), as well as GW190412 (R. Abbott et al. 2020e), GW190425 (B. P. Abbott et al. 2020b), GW190521 (R. Abbott et al. 2020f), and GW190814 (R. Abbott et al. 2020d). These candidates retain their legacy names. 1.3. Outline An outline of the remainder of this article is as follows: We briefly describe the network of ground-based GW detectors in Section 2 and their observing runs that have contributed to the GWTC-4.0 in Section 3. These sections are followed by short reviews of the evolution of the various observatories in Section 4 and of the nature of the transient sources observed in Section 5. A list of common acronyms is provided in Appendix A. Mathematical conventions used throughout the articles in this compendium are described in Appendix B. 2. The International GW Observatory Network The international ground-based GW observatory network currently comprises four primary observatories employing laser interferometric GW detectors. The four observatories are the two US-based LIGO detectors, LIGO Hanford Observatory (LHO) in Washington and LIGO Livingston Observatory 327 GWOSC event portal https://gwosc.org/eventapi. 11 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. https://gwosc.org/eventapi (LLO) in Louisiana (J. Aasi et al. 2015a); the European Virgo detector (F. Acernese et al. 2015); and the Japanese KAGRA detector (K. Somiya 2012; Y. Aso et al. 2013; T. Akutsu et al. 2021). All these detectors are enhanced Michelson inter- ferometers that sense relative changes in the lengths L1 and L2 of their two 3 km to 4 km long arms caused by passing GWs in the high-frequency band ∼10 Hz to ∼1000 Hz (K. S. Thorne 1987). Other GW frequency bands include the very low frequency band ∼1 nHz to ∼100 nHz observed by pulsar timing arrays such as the European Pulsar Timing Array (EPTA; G. Desvignes et al. 2016), the North American Nanohertz Observatory for Gravitational Waves (NANOGrav; A. Brazier et al. 2019), the Parkes Pulsar Timing Array (PPTA; M. Kerr et al. 2020), the Indian Pulsar Timing Array (InPTA; B. C. Joshi et al. 2018), and their combined consortium the International Pulsar Timing Array (IPTA; J. P. W. Verbiest et al. 2016); and the low-frequency band ∼0.1 mHz to ∼10 mHz that will be observed by the Laser Interferometer Space Antenna (LISA; M. Colpi et al. 2024). The fractional change in the relative lengths of the two optical paths of interferometric detectors, Δ(L1 − L2), induced by a GW is known as the detector strain, h = Δ(L1 − L2)/L, where L is the average arm length (Section 5.1). The sensitivity of ground-based detectors is fundamentally limited below ∼1 Hz by ground motion noise (P. R. Saulson 1984) and at high frequencies by shot noise (R. L. Forward 1978; A. Krolak et al. 1991). Significant noise sources at inter- mediate frequencies include thermal noise in the optics and their suspensions and quantum readout noise (A. Buonanno & Y.-b. Chen 2001; P. R. Saulson 2017; R. Weiss 2022). In the frequency domain, the overall detector sensitivity is characterized by the (one-sided) noise power spectral density (PSD) in strain- equivalent units, Sn( f ), with dimensions of time (Appendix B). The GEO600 GW detector (GEO) is a British–German instrument with 600 m arms located near Hannover, Germany (H. Luck et al. 2010; C. Affeldt et al. 2014; K. L. Dooley et al. 2016). This instrument is a laboratory for prototyping advanced interferometry techniques, but it also is operated in data-taking astrowatch mode when not being used for instrument science research (H. Grote 2010; K. L. Dooley et al. 2016). Astrowatch provides GW observing coverage for times when the larger detectors are not observing between observing runs and when the detectors are not taking scientific data, e.g., GEO data were used to constrain post-merger signals following the first BNS detection (B. P. Abbott et al. 2017c). 3. Observing Runs The GW observing schedule is divided into observing runs, downtime for construction and commissioning, and transi- tional engineering runs between commissioning and observing runs (B. P. Abbott et al. 2020a). Figure 1 shows a timeline of GW observations up to the end date of the time period covered by GWTC-4.0. Indicated are the observing periods of each observing run and the times when each detector was in operation. Also shown are the times when GW transient signals were detected. In order to quickly compare sensitivities of detectors, the GW community uses a fiducial range, to which a typical BNS can generally be detected. This fiducial distance assumes that an SNR of at least 8 is needed for a detection, and it approximates the BNS inspiral waveform at Newtonian order (Section 5.2). The BNS inspiral range is a volume-averaged measure of sensitivity to a signal from two 1.4 M⊙ bodies in a quasi-circular inspiral at a single-detector SNR threshold of 8 (L. S. Finn & D. F. Chernoff 1993; H.-Y. Chen et al. 2021). When a homogeneous BNS population is assumed and cosmological effects are ignored, the BNS inspiral range for a detector is determined by its noise power spectrum as R f S f df1.016 10 Mpc s , 1 n 20 1 6 0 7 3 ( ) ( )/ / = × and the sensitive volume of the detector (also when neglecting cosmological effects) is given by V = (4π/3)R3 (Appendix B). 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 GEO LHO KAGRA LLO Virgo Figure 1. The timeline of observing runs covering a time span starting from 2015 and lasting up to the beginning of O4b on 2024 April 10. The periods in which the various detectors in the network were observing are shown in this timeline, along with the typical BNS inspiral ranges for those detectors during the observing run. GEO astrowatch observing periods are shown in light gray. KAGRA observing periods during O4a, also shown in light gray, were not used for GW observational analyses. In O1 and O4a, only LHO and LLO were participating. Virgo joined these two detectors for the last month of O2 and was observing alongside them throughout O3a and O3b. At the end of O3 there was a short joint observing run, O3GK, which included GEO and KAGRA. Also shown is a timeline of the observed candidates contained in GWTC-1.0, GWTC-2.1, GWTC-3.0, and GWTC-4.0 with a probability of astrophysical origin greater than or equal to 50%. The time intervals covered by the various versions of the GWTC are bounded from above but not from below, as indicated by the arrows pointing left (see Section 1.2.1). 12 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. (This measure is taken as a simple figure of merit of sensitivity to CBCs; it does not attempt to account for the true underlying astrophysical distribution describing such systems.) If the number of BNS mergers per unit time per unit volume of space, the merger rate density of BNSs, isR, then the expected number of BNS signals seen with SNR greater than 8 in time T would be RVT . Figure 1 also gives the typical BNS inspiral range, as given in Equation (1), for each detector during each observing run. The amplitude strain noise spectrum is the square root of the (one-sided) noise PSD in strain-equivalent units S fn 1 2( )/ having dimensions of time1/2. The amplitude strain noise spectra of LHO, LLO, and Virgo during the various observing runs are shown in Figure 2. There is an overall reduction in the detector noise levels with successive observing runs resulting in increased sensitivity. Figure 2 also shows the fraction of the run duration during which different combinations of detectors were observing. Figure 3 shows the cumulative number of candidates detected versus the estimated effective time–volume hypervolume VT for the detector network. For the first two observing runs (described below), only data when two detectors were operating were searched for GWs. In this case the rate at which VT is accumulated at any observing time is given by the sensitive volume V for the second most sensitive instrument observing at that time. Beginning with the third observing run, periods during which only a single detector was observing were included in the search. During such time, the rate at which VT is accumulated is again given by the sensitive volume V = (4π/3)R3, but where R is computed from Equation (1) divided by 1.5, representing an effective SNR threshold for detection of 12 rather than 8 for single-detector observation (R. Abbott et al. 2021b). This simple estimate of VT, derived from the BNS inspiral range, is an approximate one done for a quick and convenient overview. In particular, it makes a crude approximation of whether a signal is detectable, and its numerical value is only representative of sensitivity to sources in a small region of mass space. Actual measured sensitive hypervolume 〈VT〉 values for various CBC mass regions and search methods are reported in A. G. Abac et al. (2025b). 10 24 10 23 10 22 10 21 10 20 10 19 10 18 St ra in (1 / Hz ) O1 (129.7 d) LHO (80 Mpc) LLO (70 Mpc) O2 (268.3 d) LHO (80 Mpc) LLO (100 Mpc) Virgo (30 Mpc) 101 102 103 Frequency (Hz) 10 24 10 23 10 22 10 21 10 20 10 19 10 18 St ra in (1 / Hz ) O3 (361.1 d) LHO (110 Mpc) LLO (140 Mpc) Virgo (60 Mpc) 101 102 103 Frequency (Hz) O4a (237.0 d) LHO (160 Mpc) LLO (160 Mpc) 38% 21% 13% 28% 6% 38% 1%1% 14% 12% 1% 27% 43% 14% 9% 11% 3%3% 7% 12% 53% 14% 16% 17% Figure 2. Representative noise amplitude spectral densities for LHO, LLO, and Virgo during O1 (LHO, LLO: 2015 October 24), O2 (LHO: 2017 June 10; LLO: 2017 August 6; Virgo: from F. Acernese et al. 2023a), O3 (LHO: 2020 January 4; LLO: 2019 April 29; Virgo: 2020 February 9), and O4a (LHO: 2024 January 11; LLO: 2023 November 19). The BNS inspiral ranges, defined by Equation (1), for these noise curves are given in the legend. Inset sunburst charts show the fraction of the run duration during which different combinations of detectors were observing. Gray regions in each ring indicate portions when a detector is not operating. The segments of the sunburst chart, clockwise from 12 o’clock, are LHO–LLO, LHO alone, LLO alone, and neither for observing runs involving only LHO and LLO; and LHO–LLO–Virgo, LHO–LLO, LHO– Virgo, LLO–Virgo, LHO alone, LLO alone, Virgo alone, and none for observing runs involving LHO, LLO, and Virgo. 13 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. 3.1. O1: The First Observing Run O1 consists of the time period from 2015 September 12 to 2016 January 19. O1 includes short time periods that were originally planned to be engineering time (2015 September 12 to 2015 September 18 and 2016 January 12 to 2016 January 19), but which were of sufficient quality to be included in O1. This was the first observing run with the Advanced LIGO (aLIGO) interferometers, in progress toward full aLIGO design sensitivity (B. P. Abbott et al. 2016b, 2016c), with LHO achieving a BNS range of 80Mpc and LLO a range of 70Mpc. Of the 129.7-day duration of O1, there were only 49.0 days (38%) when both LHO and LLO were observing jointly, and there were 36.2 days (28%) when neither detector was observing. The largest nonobserving periods were due to locking, the time spent bringing the interferometers from an uncontrolled state to their low-noise configuration (A. Staley et al. 2014), and environmental issues such as earthquakes, wind, and microseismic noise arising from ocean storms (A. Effler et al. 2015; B. P. Abbott et al. 2016d). Wind and microseismic noise have seasonal variation, as storms are more prevalent in winter months; LLO was more susceptible to these than LHO, mainly due to its local geophysical environment (E. J. Daw et al. 2004). Overall, a total effective hypervolume VT = 1.59 × 10−4 Gpc3 yr was accumulated during joint LHO–LLO obser- ving during O1. 3.2. O2: The Second Observing Run The O2 run was from 2016 November 30 to 2017 August 25. It was preceded by an engineering run that began on 2016 October 31 at LLO and on 2016 November 14 at LHO. The LHO and LLO detectors achieved a typical BNS range sensitivity of 80 Mpc and 100 Mpc, respectively (B. P. Abbott et al. 2017d, 2019a). However, on 2017 July 6 LHO was severely affected by a 5.8 mag earthquake in Montana, resulting in a post-earthquake sensitivity drop of approximately 10 Mpc in BNS range for the remainder of the run (B. P. Abbott et al. 2019a). The Advanced Virgo (AdV) interferometer (F. Acernese et al. 2015) joined O2 on 2017 August 1, forming a three- detector network for the last month of the run. A vacuum contamination issue required AdV to use steel wires rather than fused silica fibers to suspend the test masses, limiting the sensitivity of AdV (B. P. Abbott et al. 2019a). In O2, a 30Mpc BNS range was achieved. The LIGO detectors saw some improvement in duty factors during nonwinter months, with an almost 50% reduction in downtime due to environmental effects at both sites, though LLO lost over twice as much observing time as LHO to earthquakes, microseismic noise, and wind. O2 had a planned mid-run engineering break to effect needed repairs and to attempt improvements to the sensitivity. The Virgo instrument operated with a duty factor of approximately 85% after joining O2. There were 15 days of all three detectors observing simultaneously. Overall, a total effective hypervolume VT = 3.52 × 10−4 Gpc3 yr was accumulated during O2; of this, 3.27 × 10−4 Gpc3 yr was accumulated during joint LHO–LLO obser- ving, 2.41 × 10−5 Gpc3 yr was accumulated while all three detectors were observing, and only 3.62 × 10−7 Gpc3 yr and 4.80 × 10−7 Gpc3 yr were accumulated during joint LHO– Virgo and LLO–Virgo observing, respectively. 3.3. O3: The Third Observing Run O3 started on 2019 April 1, with a commissioning break from 2019 October 1 to 2019 November 1. This observing run was planned to continue to 2020 April 30, but the COVID-19 pandemic resulted in a suspension of observing on 2020 March 27 (R. Abbott et al. 2023). The period of O3 prior to the commissioning break is referred to as O3a, while the period after the break is referred to as O3b. KAGRA had intended to join LIGO and Virgo at the end of O3, but the early end made this impossible. Instead, KAGRA and GEO jointly observed 0.000 0.002 0.004 0.006 0.008 Cumulative effective hypervolume (Gpc³ yr) 0 50 100 150 200 250 Cu m ula tiv e nu m be r o f d et ec tio ns O1 O2 O3a O3b O4a Figure 3. The number of CBC detection candidates with a probability of astrophysical origin greater than or equal to 50% vs. the detector network’s effective surveyed hypervolume for BNS coalescences (R. Abbott et al. 2021b). The BNS effective surveyed hypervolume is a valid proxy for overall sensitivity to CBCs, though its scale is set to the case of canonical BNS signals. The colored bands indicate the different observing runs. The final data sets for O1, O2, O3a, O3b, and O4a consist of 49.0 day, 122.2 day, 149.6 day (177.1 day), 124.6 day (141.9 day) and 126.5 (196.8) days, respectively, with at least two detectors (one detector) observing. The cumulative number of probable candidates is indicated by the solid black line, while the blue line, dark-blue band, and light-blue band are the median, 50% confidence interval, and 90% confidence interval for a Poisson distribution fit to the number of candidates at the end of O4a, respectively. 14 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. for a 2-week period from 2020 April 7 to 2020 April 21 after LIGO and Virgo had suspended their observing. This joint GEO–KAGRA run (distinct from the O3 run described previously) is referred to as O3GK (R. Abbott et al. 2022). In O3, the LHO and LLO detectors achieved a BNS range of 110 Mpc and 140Mpc, respectively (A. Buikema et al. 2020). This increase in sensitivity arose from a variety of improve- ments, chief among them an increase in the input laser power, the addition of a squeezed vacuum source at the interferometer output (M. Tse et al. 2019), and mitigation of noise arising from scattered light (S. Soni et al. 2020). In addition, end-test- mass optics with lower-loss coatings, along with new reaction masses, were installed in each LIGO interferometer (S. M. Aston et al. 2012; M. Granata et al. 2020). The steel wires in AdV were replaced with fused silica fibers in preparation for O3. Along with other improvements, such as reduction of technical noises, an increase in laser power, and the installation of a squeezed vacuum source, Virgo achieved a BNS range of 60Mpc (F. Acernese et al. 2019). Over all of O3a and O3b, 361.1 days combined, there were 154.3 days (43%) of three-detector observation and only 42.1 days (12%) during which no detector was observing. The total effective hypervolume VT accumulated was 3.21 × 10−3 Gpc3 yr. Of this, 2.27 × 10−3 Gpc3 yr was accumulated during three-detector observations, 7.20 × 10−4 Gpc3 yr when LHO and LLO were observing, 4.09 × 10−5 Gpc3 yr when LHO and Virgo were observing, and 5.03 × 10−5 Gpc3 yr when LLO and Virgo were observing. The amount accumulated with only a single detector observing was 4.47 × 10−5 Gpc3 yr, 7.47 × 10−5 Gpc3 yr, and 9.72 × 10−6 Gpc3 yr for LHO, LLO, and Virgo, respectively. The first operation of the KAGRA detector in an initial configuration with a simple Michelson interferometer occurred in 2016 March (T. Akutsu et al. 2018). In 2019 August, the first lock of the Fabry–Perot Michelson interferometer was achieved, with power recycling accomplished in 2020 January. By the end of 2020 March, KAGRA obtained a BNS range of approximately 1Mpc (H. Abe et al. 2023), and although the LIGO and Virgo instruments had ended their O3 run, KAGRA was operated jointly with GEO, which had a comparable BNS range, in O3GK yielding 6.4 days of joint observing time. 3.4. O4: The Fourth Observing Run O4 began on 2023 May 24 at 15:00:00 UTC. This run is again divided into parts: the fourth observing run (O4a) ended on 2024 January 16 at 16:00:00 UTC and was followed by a commissioning break; the fourth observing run (O4b) started on 2024 April 10 at 15:00:00 UTC. The O4b period continued until 2025 January 28 17:00:00 UTC, the original intended end of O4; however, it was decided to continue observing into a third part of the fourth observing run (O4c), which ended on 2025 November 18 at 16:00 UTC. The period covered by GWTC-4.0 contains events that occurred in O4a and earlier observing runs only (see Section 1.2.1). O4b and O4c analyses are underway and will be included in future versions of the GWTC. The two LIGO detectors were observing during O4a, both having a BNS range of approximately 160Mpc. During the 237.0 days, there were 126.5 days (53%) of two-detector joint observation and 40.2 days (17%) when neither of the LIGO detectors was observing. Virgo did not join joint observation until O4b in order to continue commissioning to address a damaged mirror that limited performance and to improve sensitivity. KAGRA also continued commissioning to improve sensitivity, with the goal of joining O4 toward the end of the run. During O4a, the total effective hypervolume VT accumu- lated was 5.28 × 10−3 Gpc3 yr. This is divided into 3.85 × 10−4 Gpc3 yr during which LHO alone was observing, 4.57 × 10−4 Gpc3 yr during which LLO alone was observing, and 4.44 × 10−3 Gpc3 yr during which both detectors were observing. The timeline for O5 is being assessed in order to maximize the scientific output of the global network. Updates to the planned observing schedule will be provided as soon as such decisions are made.328 4. Observatory Evolution The advanced-detector era is characterized by a series of technological improvements from the initial detectors that deliver higher sensitivity and greater BNS range, which made possible the era of GW observation. Some of the key instrument science elements of the advanced era detectors are (i) increases in the input laser power entering the interferometer and to the circulating power in the interferom- eter cavities (a higher power in the arms produced a lower quantum-shot-noise-limited sensitivity above ∼200 Hz); (ii) increases in test-mass mirror size to accommodate larger beams, which mitigates coating thermal noise and heavier masses to reduce inertial and quantum back-action effects; (iii) implementation of signal recycling (B. J. Meers 1988) in addition to power recycling (R. W. P. Drever 1983), which alters the frequency band of the detectors’ sensitivity (typically to give broader-band sensitivity); (iv) implementation of monolithic test-mass suspensions, which reduces the suspen- sion thermal noise in the detectors’ sensitivity band by using the same low mechanical loss material (fused silica for LIGO and Virgo) for the suspension fibers as for the mirror substrate, and low-loss jointing techniques and thermoelastic nulling (S. M. Aston et al. 2012; F. Travasso 2018); (v) improved passive and active seismic isolation systems and sensors to reduce ground motion coupling to the detector and to damp suspension modes (S. Braccini et al. 2005; F. Matichard et al. 2015; S. J. Cooper et al. 2023); and (vi) improved low thermal noise, low-absorption, high-reflectivity mirror coatings (G. M. Harry et al. 2007; M. Granata et al. 2020). Throughout the advanced-detector era of GW observation, the LIGO and Virgo detectors have undergone a series of performance-improving detector upgrades and commissioning activities, details of which are given in this section. Detector upgrades include the installation of new hardware or upgrades to existing hardware in a detector. Examples of detector upgrades include the installation of new laser systems to provide higher power into the interferometer, installation of baffles to mitigate scattered light, and the injection of squeezed light to manipulate the quantum-noise-limited sensitivity of the detectors (F. Acernese et al. 2019; M. Tse et al. 2019). Commissioning activities cover a range of improvements to sensitivity and observing uptime of the instruments from targeted noise-hunting activities that remove glitches, lines, 328 LVK observing run plans https://observing.docs.ligo.org/plan. 15 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. https://observing.docs.ligo.org/plan and broadband noise, to improved control schemes that mitigate instabilities and improve detector robustness. Alongside this has been the effort to build and commission the KAGRA detector utilizing advanced technologies such as cryogenic cooling of the test masses and an underground location. This schedule of planned upgrades and commissioning activities between observing runs ensures that the maximal science output is achieved from the network. In terms of valuable scientific output, a successful upgraded detector that has been offline for a period of time rapidly overtakes a non-upgraded detector in continuous observational mode in terms of number of significant detections and the resolution and sky localization of high-interest signals. The aLIGO and AdV detectors are designed to be dual- recycled Fabry–Perot Michelson interferometers with ortho- gonal kilometer-scale arms (F. Acernese et al. 2015; J. Aasi et al. 2015a). Each arm contains a Fabry–Perot optical cavity, and a beam splitter at the corner between the arms forms a Michelson interferometer that measures the change in the relative phase of the light induced by changes in the lengths of these cavities (K. S. Thorne 1987; J. Y. Vinet et al. 1988). Additional power-recycling and signal-recycling cavities are created by adding mirrors in the symmetric and antisymmetric ports of the interferometer. These improve sensitivity by building up the light power on the beam splitter and beneficially modifying the response of the interferometer, respectively (B. J. Meers 1988). The input and end mirrors on each of the Fabry–Perot cavities are the test masses whose separations are affected by GWs. The mirrors are isolated by multistage pendulums that suppress the ground motion by more than 10 orders of magnitude at frequencies around 10 Hz. Monolithic fused silica fibers are used on the bottom stage of the suspension system to suppress thermal noise, and the mirrors themselves are fused silica substrates with low-loss, highly reflective coatings (S. M. Aston et al. 2012). Ground-based interferometers generally have the same fundamental limiting noise sources (P. R. Saulson 2017; R. Weiss 2022), with the response of each detector and the exact extent to which each noise limits sensitivity being specific to the detailed design of each detector. At low observational frequency below ∼10Hz the detectors are limited by a combination of seismic noise, gravity gradient noise, suspension thermal noise, and quantum radiation pressure noise. Thermal noise in the mirror optical coatings is a significant noise source at intermediate frequencies ∼50 Hz to ∼200 Hz (G. M. Harry et al. 2007), and at high frequencies, above ∼200Hz, sensitivity is limited by the quantum shot noise. In addition to these fundamental noise sources, the detectors are also limited by technical noise. This includes scattered- light noise, which occurs when some fraction of light is deflected from the interferometer beam path and is incident on another moving surface, varying the phase of the light; this couples noise into the interferometer readout if part of this light is reflected back into the main beam (T. Accadia et al. 2010; D. J. Ottaway et al. 2012). Interferometer control-system noise is when signals couple between the multiple feedback loops that control the degrees of freedom of the interferometer and requires complicated optimization of control loop para- meters to mitigate (A. Buikema et al. 2020). Laser noise due to fluctuations in the frequency, intensity, and pointing of the laser beam entering the interferometer is reduced with dedicated multistage stabilization systems to a level such that it does not impact the sensitivity of the detectors; however, suboptimal tuning of these stabilization systems can lead to laser noise affecting sensitivity (C. Cahillane et al. 2021). Environmental noise is caused when environmental effects in the vicinity of the interferometer (e.g., seismic activity) couple into the measurement of the interferometer strain signal (F. Acernese et al. 2006; A. Effler et al. 2015; I. Fiori et al. 2020; P. Nguyen et al. 2021; A. Helmling-Cornell et al. 2024). Detector commissioning seeks to mitigate such nonfunda- mental noise sources. The key parameters of the LIGO, Virgo, KAGRA, and GEO detectors across the advanced era observing runs are given in Table 1. The specific evolution of each detector in terms of Table 1 Selected Optical and Physical Parameters of the LIGO Hanford (LHO), LIGO Livingston (LLO), Virgo, KAGRA, and GEO600 (GEO) Interferometers throughout the Advanced-detector Era Observing Period Interferometer Input Laser Power Power-recycling Gain Signal Recycling Squeezing Suspension Type O1 LHO 21 W 38 ✓ × Silica LLO 22 W 38 ✓ × Silica O2 LHO 26 W 40 ✓ × Silica LLO 25 W 36 ✓ × Silica Virgo 10 W 38 × × Steel O3a LHO 34 W 44 ✓ ✓ Silica LLO 44 W 47 ✓ ✓ Silica Virgo 18 W 36 × ✓ Silica O3b LHO 34 W 44 ✓ ✓ Silica LLO 40 W 42 ✓ ✓ Silica Virgo 26 W 34 × ✓ Silica O3GK GEO 3 W 1000 ✓ ✓ Silica KAGRA 5 W 12 × × Sapphire O4a LHO 57 W 50 ✓ ✓ Silica LLO 64 W 35 ✓ ✓ Silica Note. The input laser power is the power that would be measured at the power-recycling mirror (after the input mode cleaner) and is an estimate of the maximum level typically achieved during an observing period. Suspension types are monolithic fused silica fibers, sapphire fibers, or steel wires. 16 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. detector upgrades and improvements is detailed in the remainder of this section. 4.1. LIGO Hanford and Livingston Observatories LIGO is a US national facility comprising two US-based interferometric detectors in Hanford, Washington (LHO), and Livingston, Louisiana (LLO), each with 4 km arms. LIGO construction began in 1994. From 2002 to 2010, initial power- recycled Fabry–Perot Michelson interferometers were oper- ated at these sites in a series of science runs S1−S6 (B. P. Abbott et al. 2009; J. Aasi et al. 2015b). During this period, LIGO also operated a second interferometer with 2 km arms at the Hanford site. Subsequently the aLIGO project resulted in a major overhaul of the interferometers to improve the capabilities of the detectors (J. Aasi et al. 2015a), leading up to O1 and the first observation of GWs. Across the observing runs certain areas have been the main focus of much of the detector improvement effort: (i) increasing the arm cavity power by increasing the injected laser power and the power-recycling gain while achieving stable operation, (ii) mitigation of scattered-light sources and coupling mechanisms, and (iii) reduction of quantum noise with addition of a squeezed-light system for O3 and the following improvements to the quantum-enhancement factor. Both aLIGO detectors are operated with a lower injected laser power and lower power-recycling gain than the design goal (J. Aasi et al. 2015a). The full amount of available laser power cannot be fully utilized, due to issues with maintaining long-duration stable locking of the interferometer owing to angular instabilities and point absorbers in the test-mass mirrors (A. F. Brooks et al. 2021). This issue was the focus of commissioning efforts to continually improve the operating power in the cavity by optimizing the interferometer control loops (A. Buikema et al. 2020) and reducing the presence of point absorbers in the mirrors. Stray-light control can be achieved by the addition of baffles to block unwanted beam paths and with active control of known scattered-light paths. The addition of a squeezed vacuum source at the interferom- eter’s output alters the quantum noise in the interferometer and, with the inclusion of a filter cavity, can produce frequency-dependent squeezing, which can be used to surpass the standard quantum limit on sensitivity of a laser interferometer (M. Tse et al. 2019; D. Ganapathy et al. 2023). 4.1.1. O1 The sensitivity and limiting noise sources of the LIGO detectors during O1 are described in B. P. Abbott et al. (2016c). Figure 2 shows a representative amplitude spectral density of the strain noise and the BNS range. In O1, the typical input power entering the power-recycling cavity was 21W in LHO and 22W in LLO, circulation of laser light in the power-recycling cavity increases the power on the beam splitter to be a factor of 38 times greater (the power-recycling gain), and a further increase in circulating power by a factor of 144 is achieved in the arms by the Fabry–Perot cavities. The laser input power and power-recycling gain during O1 and the later observing runs are given in Table 1, alongside other detector parameters. An example of commissioning improve- ment is the investigation at LLO during O1 of recurring changes in the BNS range from 65 Mpc to 60Mpc. By searching for correlation between the detector range and the hundreds of data channels recorded by aLIGO, it was found that the issue was caused by a malfunctioning temperature sensor. This sensor was replaced, resulting in a stabler increased range (M. Walker et al. 2018). 4.1.2. O2 After O1, several improvements were made to both LIGO instruments (B. P. Abbott et al. 2017d). Detector upgrades included installation of new mass dampers on the end-test- mass suspensions to dampen mechanical modes, improving the stabilization of laser intensity, and installing a new output Faraday isolator and higher quantum-efficiency photodiodes at the output port to improve signal detection efficiency in the readout system. Mitigation of scattered-light sources and other improvements to the detector sensitivity throughout O2 resulted in a BNS range improvement to 100Mpc by the end of the run (D. Davis et al. 2021). Commissioning tests during O2 on the LHO detector to increase the laser power to 50W did not result in an overall improvement in performance of the 80Mpc BNS range at the end of O1, due to point absorbers on one of the input test-mass optics, so the detector operated with 30W input power. After O2, it was demonstrated that the use of witness channels to perform noise subtraction on the strain data was able to increase the BNS range by 20% (D. Davis et al. 2019; J. C. Driggers et al. 2019). 4.1.3. O3 Leading up to O3, several upgrades were made to the LIGO instruments (A. Buikema et al. 2020). The most significant was the installation of an in-vacuum squeezed-light injection system at each site to inject squeezed vacuum into the interferometers to reduce shot noise at frequencies above 50 Hz (M. Tse et al. 2019). The squeezer works by optically pumping a nonlinear crystal to modify the distribution of the quantum vacuum state that enters the interferometer (C. M. Caves 1981; L. Barsotti et al. 2019). Between O3a and O3b, adjustments to the squeezing subsystem produced large sensitivity improvements. Among these were the installation of higher-power laser amplifiers with stable operation and output power over 70W (N. Bode et al. 2020). A program of installation of optical baffles was completed to improve stray-light control. The correlation of microseismic activity with scattered-light noise was deter- mined to be primarily caused by a scattered-light path arising from large relative motion between the end test mass and the reaction mass that is immediately behind it (S. Soni et al. 2020). A control loop that makes the reaction mass follow the end mass, implemented on 2024 January 7 at LLO and 2024 January 14 2024 at LHO, reduced the relative motion and mitigated the scattered-light noise (D. Davis et al. 2021). At LHO, wind fences were installed to mitigate ground tilt induced by wind on the buildings (P. Nguyen et al. 2021). 4.1.4. O4a Several upgrades were implemented at LHO and LLO to improve the quantum-limited sensitivity of the detectors via improved quantum squeezing and higher intracavity power (A. G. Abac et al. 2024a). Further upgrades to the laser amplification system were implemented with stable operation and output power over 140W (N. Bode et al. 2020). A new vacuum system to house a 300 m filter cavity was built at both 17 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. detectors, along with an upgraded squeezing injection system to allow the injection of frequency-dependent squeezed vacuum to achieve quantum noise reduction across the detection frequency band (D. Ganapathy et al. 2023; W. Jia et al. 2024). Squeezing levels in O4a reached 5.8 dB at LLO and 4.6 dB at LHO, compared to the 2 dB to 3 dB achieved in O3 (E. Capote et al. 2025). Test-mass mirrors were replaced at both observatories to remove point defects on the mirrors that contributed to control challenges and excess noise (A. Buikema et al. 2020). This involved a replacement of both end test masses at LLO and the input y-arm test mass at LHO. Replacing these test masses allowed both observatories to approximately double the input power compared to O3, further improving the quantum-limited sensitivity of the detectors, due to higher circulating power in the Fabry–Perot arm cavities (A. Buikema et al. 2020; E. Capote et al. 2025). Other upgrades to the LIGO detectors include improvements to the electronics in the GW signal readout chain, damping of baffles to mitigate scattered light, and improvements to electronics grounding (E. Capote et al. 2025; S. Soni et al. 2025). The photodetector transimpedance amplifiers were improved ahead of O4a using a design tested at GEO, resulting in a factor of 10 reduction in dark noise compared to O3 (H. Grote et al. 2016). At both LIGO detectors, a septum window separating two vacuum volumes housing the output optics was removed, significantly reducing the coupling of acoustic noise. Baffles along the arm cavity and around vacuum pumps were previously identified to couple excess scattered light in O3 and were damped to reduce their motion and therefore shift the frequency of up-converted scattered light out of the sensitive band. Finally, injections into the building electronics ground demonstrated that many spectral features in the strain at LHO were the result of a fluctuating ground potential (E. Capote et al. 2025; S. Soni et al. 2025). The resistance to ground was reduced for several electronics chassis around the detector. Additionally, the voltage biases of the test-mass electrostatic drives were adjusted to minimize the electronics noise coupling further (E. Capote et al. 2025). Detector commissioning ahead of O4a also focused on optimization of the auxiliary controls to reduce technical noise that limited the detectors at low frequency in O3 (A. Buikema et al. 2020). Alignment control noise was reduced by a factor of 10 and length control noise by a factor of two at both detectors near 20 Hz (A. Buikema et al. 2020; E. Capote et al. 2025). Significant improvements to the controls included the upgrade to a camera servo system that requires no line injection to sense the alignment of the main detector optics (E. Capote et al. 2025). Suspension local control loops were reoptimized to focus on noise suppression above 5 Hz, reducing both noise directly coupled to the strain and noise that couples indirectly through the length and alignment controls (E. Capote et al. 2025). Both detectors were also limited by unmitigated beam jitter noise that was well witnessed by auxiliary sensors (E. Capote et al. 2025). As such, front-end infrastructure using the non-stationary estima- tion and noise subtraction (NonSENS) code (G. Vajente 2018) was implemented to perform noise cleaning in low latency, increasing detector sensitivity by up to 5Mpc in BNS range (G. Vajente et al. 2020; G. Vajente 2022; E. Capote et al. 2025). 4.1.5. Beyond O4 Looking to the future, there is ongoing construction of LIGO-India (T. Souradeep et al. 2017), a third LIGO interferometer to be built in the Hingoli district of Maharash- tra, India. This facility will be based on aLIGO hardware and design, and its location will provide a significant improvement in the sky localization of GW sources (C. Pankow et al. 2020; M. Saleem et al. 2022; S. Pandey et al. 2025). In parallel, there are plans underway to upgrade the existing LIGO detectors (and eventually LIGO-India) to Advanced+ LIGO (A+) sensitivity (B. P. Abbott et al. 2020a; S. J. Cooper et al. 2023). The A+ upgrade to the LIGO detectors is a series of detector upgrades utilizing improved technology that has been developed in parallel to the observing runs. The inclusion of frequency-dependent squeezing was originally planned as an A+ upgrade but was implemented ahead of O4a at both sites (E. Capote et al. 2025). Other A+ upgrades, which will be implemented for future observing runs, include new optics with lower noise and loss, improved sensors for controlling the mirrors, a new pre-mode cleaner to reduce beam jitter noise, improved output mode cleaners with lower loss, and a balanced homodyne readout system that allows for better readout control of the interferometer signal. A post-O5 upgrade, referred to as LIGO A♯ (A♯), explores more transformative changes in detector design, with the goal of increasing the sensitivity to the limits of what is possible with the existing infrastructure of the LIGO detectors (P. Fritschel et al. 2024). Detector improvements that facilitate the achievement of the A♯ sensitivity include the upgrade of the laser injection system to deliver more power into the interferometer and an improved system for the thermal compensation of the test-mass mirrors. The test-mass mirrors will be replaced with heavier masses with improved optical coatings, and A♯ targets an improved exploitation of the quantum noise reduction from the squeezed-light system. The A♯ configurations are natural outgrowths of A+ configurations and will serve as pathfinders for the next-generation Cosmic Explorer concept (M. Evans et al. 2021). Additionally, it has much technological overlap with Advanced Virgo+ (AdV+) and Virgo_nEXT (Section 4.2), which presents the possibility of collaborating on developing these technologies. 4.2. Virgo Observatory The Virgo interferometer, located in Cascina (Italy), is the largest European GW detector, designed in its AdV Phase I as a 3 km dual-recycled Fabry–Perot Michelson interferometer (F. Acernese et al. 2015). Construction of Virgo started in 1997 and was completed in 2003 (F. Acernese et al. 2005). Four science runs of the initial Virgo interferometer, VSR1 −VSR4, took place between 2007 and 2011. These were followed by upgrades leading to the AdV design operated during O2 and O3. Subsequently, further upgrades leading to AdV+ were planned to take place in two phases, the first for operation during O4 and the second for operation during O5. A proposed next-generation upgrade planned post-O5, Virgo_nEXT, would provide further sensitivity by pushing current facilities to their limit and would serve as a pathfinder for future ground-based GW detectors. The first-generation Virgo detector (T. Accadia et al. 2012a) observed jointly with the initial LIGO detector’s fourth and fifth science runs. After several years of commissioning, from 18 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. 2007 May to 2007 October the first scientific data run VSR1 (along with LIGO) took place, for which a BNS range of 4Mpc was achieved (F. Acernese et al. 2008). At this stage, Virgo was a power-recycled Fabry–Perot Michelson inter- ferometer with a 20W laser source. The second Virgo science run, VSR2 (also along with LIGO), from 2009 July to 2010 January (T. Accadia & B. L. Swinkels 2010), was preceded by a set of major improvements to mitigate scattered light and to improve the light injection system. The replacement of the four payloads in the Fabry–Perot cavities was the major improvement in preparation for the third Virgo science run VSR3, from 2010 July to 2010 October (T. Accadia et al. 2012b). Issues arising from thermal noise due to improperly aligned suspension wires and degraded contrast resulting from differing radii of mirror curvature were addressed leading up to VSR4, from 2011 June to 2011 October, during which Virgo achieved a BNS range of 12Mpc. While the three previous VSRs were aligned with initial LIGO science runs, Virgo took data during this run together with GEO. The main upgrade consisted of the installation of the central heating radius of curvature correction (CHRoCC) on both end mirrors, which allowed the radius of curvature of the mirrors to be controlled in real time (T. Accadia et al. 2013). This system was designed to correct the thermal lensing effect in the mirrors, which had been a significant source of noise in the interferometer. Virgo stopped observing in 2011 for the AdV upgrade. 4.2.1. O2 After these four science runs, major modifications were made to the optical layout to increase the broadband sensitivity by up to an order of magnitude (B. P. Abbott et al. 2017e). These upgrades marked the transition from Virgo, a first- generation interferometer, to AdV, a second-generation GW detector (F. Acernese et al. 2015). The installation of AdV started in 2011 and was completed in 2016. AdV was planned as a dual-recycled interferometer with 125W entering the interferometer, though signal recycling was not implemented until O4. The main improvements included a ∼3-fold increase in the arm cavity finesse (a measure of how long light stays within the cavity), 42 kg fused silica test masses with ultralow absorption and high homogeneity, new stray-light control using diaphragm baffles and a vibration isolation system, an improved thermal compensation system with double axicon CO2 laser projectors and ring heaters, an improved output mode cleaner with two cascaded monolithic bow-tie resona- tors, and a new design of payloads triggered by the need to suspend heavier mirrors, baffles, and compensation plates. The several months of commissioning that started at the end of 2016 October achieved the target early-stage BNS range of 8Mpc in 2017 April with 13 W input laser power. After an intense campaign of noise investigations, AdV sensitivity was considered sufficient to join aLIGO during the O2 observing run in 2017 August (F. Acernese et al. 2018). During O2, the AdV BNS range reached 30Mpc. As noted in Section 3.2, the low-frequency Virgo sensitivity during O2 was limited by thermal noise from metallic suspension wires, which were implemented as a fallback option owing to the frequent failure of monolithic suspensions after the installation of the main AdV upgrades. 4.2.2. O3 The most important Virgo upgrades for O3 were the mitigation of suspension thermal noise by installation of monolithic suspensions and the mitigation of quantum noise by increase of input laser power and by injection of frequency- independent squeezing. An in-air optical parametric amplifier was implemented in the Virgo interferometer before the start of O3a, and squeezing injections were maintained during the whole of O3, with a 3 dB gain in sensitivity at high frequency (F. Acernese et al. 2019, 2020). Throughout O3, work was continuously carried out to improve the Virgo sensitivity in parallel with the ongoing data taking. Dedicated tests were made during planned breaks in operation (commissioning, calibration, and maintenance), and in-depth data analysis of these tests was performed between breaks to ensure continual improvement. In particular, the 1-month commissioning break between the O3a and O3b observing periods was used to get a better understanding of the Virgo sensitivity and of some of its main limiting noises (R. Abbott et al. 2023). This effort culminated during the last 3 months of O3b. The most significant change to the Virgo configuration between O3a and O3b was the increase of the input power from 18 W to 26 W. As with the LIGO detectors, it was found that the optical losses of the arms increased following the increase of the input power. New high quantum efficiency photodiodes that had been installed at the output (detection) port of the interferometer prior to the start of O3a were found to increase the electronics noise at low frequency. These were improved at the end of 2020 January during a maintenance period, by replacing pre- amplifiers. The electronic noise disappeared completely, leading to a BNS inspiral range gain of ∼2Mpc. Finally, in the period from the end of 2020 January to the beginning of 2020 February the alignment was improved for the injection of the squeezed light into the interferometer (F. Acernese et al. 2019, 2020), a critical parameter of the low- frequency sensitivity. By mitigating scattered-light noise, the BNS range increased by 1 Mpc to 2 Mpc. 4.2.3. O4 The AdV+ interferometer layout (F. Acernese et al. 2023b) was designed as a two-step project, for O4 (Phase I) and O5 (Phase II), with the aim to reduce quantum and thermal noise, respectively. The main upgrades for O4 included a new high- power fiber laser amplifier replacing the former solid-state amplifier, to reach 125W; the implementation of an additional recycling cavity at the output of the interferometer, the signal- recycling cavity, to broaden the sensitivity band; an output mode cleaner with increased finesse; a frequency-dependent squeezing system to reduce quantum noise at all frequencies; a network of seismic and acoustic sensors for Newtonian noise monitoring; and a Newtonian calibrator for improved calibra- tion accuracy. These upgrades, while meant to improve the detector sensitivity, also increased the difficulties in control- ling the interferometer in the presence of optical defects (from both thermal aberration and cold defects), due to the marginal stability of the Virgo recycling cavities (F. Acernese et al. 2023b). Efforts were put forward to control the dual-recycled interferometer’s sensitivity to small defects. For instance, a CHRoCC (T. Accadia et al. 2013) was installed in 2022 to 19 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. create a thermal lens on the pick-off plate so as to match the power-recycling cavity to the arm cavities. These turned out not to be enough to have a stable interferometer working at the targeted laser power. High-order modes were resonant in the cavities, and these strongly complicated stable operations. The laser input power was decreased to 18W to improve interferometer control and stability. The various changes on the configuration and attempts to reach stable operations prolonged the anticipated commissioning period between runs. Thus, AdV+ could not join for the O4a observing run. Instead, continued commissioning allowed AdV+ to reach a BNS range of 54Mpc, with which it joined O4b. 4.3. KAGRA Observatory The KAGRA interferometer, situated in Japan’s Kamioka mine, is the only large-scale GW detector in East Asia. It is designed as a cryogenic, 3 km, dual-recycled Fabry–Perot Michelson interferometer. The KAGRA project was funded in 2010, construction began in 2012, and tunnel excavation was completed in 2014 (T. Akutsu et al. 2021). Following installation and assembly in the tunnel, two operations using temporary detector configurations served as key project milestones: the initial-phase KAGRA (iKAGRA) operation in 2016 April (T. Akutsu et al. 2018), and the baseline-design KAGRA (bKAGRA) phase-1 operation in 2018 April. During the bKAGRA phase-1 operation, both cryogenic technology and the large-scale vibration isolation systems of KAGRA were successfully demonstrated (T. Akutsu et al. 2019). By the summer of 2019, the primary installation of instruments was completed, allowing for the commissioning of the detector to begin immediately. In 2019 October, a memorandum of agreement forming the LVK was signed, and the LVK international observation network was launched (P. Brady et al. 2019). After that, the commissioning phase continued until 2020 March, marking the commencement of the detector’s scientific operation. 4.3.1. O3GK O3GK was a joint observation conducted with the GEO detector in 2020 April (H. Abe et al. 2023), just after the early termination of O3b. The O3GK operation marked the first joint observation between KAGRA and GEO. This collaboration aimed to improve the detection capabilities by combining data from both detectors. The optical configuration used during O3GK was a power-recycled Fabry–Perot Michelson inter- ferometer, with one room-temperature sapphire test mass and the others set around 250 K. During the O3GK operation, KAGRA observed for approximately 7.3 days, with a strain sensitivity of 3.0 × 10−22 Hz at 250 Hz. The BNS range was about 0.7 Mpc (R. Abbott et al. 2022). The sensitivity of KAGRA during O3GK was influenced by various noise sources, including sensor noise from local controls of the vibration isolation systems, acoustic noise, shot noise, and laser frequency noise (H. Abe et al. 2023). Understanding these noise contributions was crucial for planning future improvements to the detector’s sensitivity. To enhance its performance, KAGRA plans to implement hardware upgrades and refine its noise mitigation strategies. These improvements aim to extend the detection range and increase the precision of GW observations. 4.3.2. O4 On 2024 January 1 a 7.5 mag earthquake struck near the KAGRA site, marking the most significant seismic event in the area in the past century. As a result, 10 seismic noise isolators sustained damage but have since been restored. While further investigation and improvements were still needed for some vacuum and facility-related components, partial commission- ing began in 2024 July. By 2024 October, all earthquake- related repairs were completed, followed by noise reduction efforts across multiple domains. During the October commis- sioning, KAGRA achieved a significant improvement on the BNS range using a power-recycled Fabry–Perot Michelson interferometer configuration with DC readout. Further com- missioning tasks have been performed, including reduction of suspension local control noise through updates to the control filters, reduction of photodiode dark noise below the shot noise level by mitigating electrical coupling from other electronic devices, reduction of quantum shot noise by increasing the laser power to above 10W, reduction of thermal noise by cooling the mirrors and their suspensions to below 100 K, and reduction of frequency noise and acoustic noise through hardware improvements and control system updates. Follow- ing these improvements, KAGRA began operating in O4c on 2025 June 11. 4.4. GEO Observatory The GEO detector is a Michelson interferometer with two nearly orthogonal 600 m arms (B. Willke et al. 2002). Rather than Fabry–Perot cavities, GEO uses folding in the arms, in which the light traverses each arm twice, to give an optical length of 1200 m for each arm. GEO is sensitive to GWs in the 50 Hz to 1.5 kHz frequency range. GEO began operation in 2001. From 2009 to 2014, it underwent a series of upgrades, the GEO-HF program, that resulted in a factor of 4 improvement in sensitivity at high frequencies (H. Grote 2010; K. L. Dooley et al. 2016). In 2010, squeezed vacuum injection was first applied in GEO (J. Abadie et al. 2011), and the first long-term application of squeezing was demonstrated in GEO in 2011 (H. Grote et al. 2013). Subsequently, 6 dB of squeezing (equivalent to a factor of 4 increase in light power) has been achieved (J. Lough et al. 2021). GEO has served as an advanced development center and test bed for technologies that were subsequently incorporated in larger detectors (C. Affeldt et al. 2014), such as dual-recycling (G. Heinzel et al. 2002), monolithic suspension (S. Goßler 2004), thermal compensation (H. Luck et al. 2004), homodyne detection (DC readout; S. Hild et al. 2009), and squeezed-light injection (J. Abadie et al. 2011). 4.4.1. Astrowatch Following the first-generation LIGO and Virgo science runs, GEO embarked on an astrowatch program of near-continual data collection (when the detector is not being used for instrument science research) as the sole observing detector (K. L. Dooley 2015). This mode of operation has continued since 2007 and allows for searches for GWs associated with external events such as gamma-ray bursts, neutrino detections, or nearby supernovae, occurring outside of other detectors’ observing periods (e.g., A. G. Abac et al. 2024b). 20 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. 4.4.2. O3GK As described in Section 3.3, a 2-week-long joint observing run with the GEO and KAGRA detectors took place in 2020 April, during which GEO operated with an 80% duty cycle (10.9 days of operation) and a BNS range of 1.1 Mpc (R. Abbott et al. 2022). The laser power injected was about 3W, which led to about 3 kW of circulating power in the power-recycling cavity, or 1.5 kW of circulating power per arm (C. Affeldt et al. 2014; K. L. Dooley et al. 2016). Bilinear noise subtraction resulted in modest improvement in sensitiv- ity and data quality (N. Mukund et al. 2020). Since GEO and KAGRA had similar sensitivity during O3GK, this joint run enabled searches for GW transient signals occurring simulta- neously in both detectors, though no significant events were observed (R. Abbott et al. 2022). 5. Review of Observed Transient Sources The GWTC includes all observed transient GW candidates reported by the LVK. It is most likely that the significant candidates in GWTC-4.0 have an astrophysical origin and were produced by CBC sources (the remaining less significant candidates are largely nonastrophysical). This section provides a foundational overview of transient GW signals, especially those from CBCs, for use in interpreting the catalog’s contents and for reference in companion articles. We first provide a short overview of the basic physics of GWs and then provide an introduction to the CBC sources to be used as a reference for companion articles. Additional detail can also be found in M. Maggiore (2007, 2018) and J. D. E. Creighton & W. G. Anderson (2011). 5.1. Gravitational Waves In metric theories of gravity, such as GR, the local gravitational field can be described in terms of six independent degrees of freedom that represent the relative accelerations of a collection of nearby freely falling observers (F. A. E. Pirani 1956; C. W. Misner et al. 1973). Plane wave solutions to the linearized gravitational field equations (A. Einstein 1916) represent the weak GWs in the far-field region (where the observer is far from the source and the gravitational field is treated as a perturbation to Minkowski spacetime) that are observed by GW detectors. The vacuum Einstein field equations of GR then further restrict the degrees of freedom of the plane wave solutions to two transverse polarizations that propagate at the speed of light (A. S. Eddington 1922). These are called the plus (+) polarization and the cross (×) polarization. In a suitably chosen set of coordinates, known as the transverse-traceless gauge (C. W. Misner et al. 1973; K. S. Thorne 1987), which is akin to the radiation gauge in classical electromagnetism, the perturbation to the Min- kowski metric for these two polarizations is given by the two functions of spacetime h+ and h×, respectively. These polarizations represent two spin-2 purely transverse tensor modes (S. Weinberg 1972). The transverse-traceless gauge is a useful choice because world lines that are the histories of fixed points in these spatial coordinates are geodesics of the perturbed spacetime (J. B. Hartle 2021). Thus, changes in time in the metrical distance between fixed spatial coordinate locations, which is described by the time derivatives of h+ and h×, represent the deviation of the geodesics at these locations. Therefore, h+ and h× are the physical (observable) degrees of freedom of a GW. From an observational point of view, GW signals are broadly classified as persistent or transient. The main classes of persistent GWs include quasi-monochromatic signals, e.g., as produced by rotating NSs having a nonaxisymmetric mass distribution (M. Zimmermann & E. Szedenits 1979), and continuous stochastic superpositions of GWs from numerous unresolved independent sources (J. D. Romano & N. J. Corn- ish 2017). Here we focus on the transient signals that are cataloged in GWTC. 5.1.1. Transient GW Signals A transient GW is one that registers a signal of short duration (much less than the duration of the observing run) within the sensitivity band of the GW detectors. Such GWs can be characterized by their geocentric arrival time tgeo, the time at which some fiducial point in the GW’s waveform (e.g., its peak amplitude) passes through Earth’s center. We expect that transient GWs will be observed as plane waves originating from a particular point in the sky, usually given in terms of the equatorial celestial coordinate system of R.A. α and decl. δ, with a normal vector −N along this line of sight. A key task for multimessenger astronomy with GWs is the reconstruction of the source location, which facilitates follow-up with other astronomical facilities (B. P. Abbott et al. 2020a). A network of detectors spaced at different locations on Earth can observe the difference in the time of arrival of the fiducial point in the waveform arising from the propagation of the plane wave across Earth and thereby reconstruct the direction of propagation N (S. Fairhurst 2009; J. D. E. Creighton & W. G. Anderson 2011; S. Fairhurst 2011; L. P. Singer & L. R. Price 2016). Such triangulation is the main way in which the sources of transient GWs are localized. Hence, uncertainty in the sky location of the source, ΔΩ, partially results from the measurement uncertainty of the arrival time in each detector (S. Fairhurst 2011). A single detector provides no ability to determine the sky location of a source for transient signals lasting much less than a day and having wavelengths much longer than the size of the detector (as is the case for all candidates reported in GWTC-4.0); however, with two detectors, the difference in times of arrival identifies a circle on the celestial sphere, centered on the axis separating the detectors, on which the wave’s origin may lie. The presence of a third detector whose location is not colinear with the other two then identifies the source position to one of two points on the sky mirrored across the plane containing these three detectors. A fourth detector, not coplanar with the other three, finally resolves the location of the source to a single point on the sky. Additional localization information can be provided by coherently combining the observed GW signals from an array of detectors as described below. For some types of transient sources having known GW emission, such as CBCs, it is also possible to estimate the distance to the source from measurements of the wave amplitude (C. Cutler & E. E. Flanagan 1994). In such cases, there is a volume localization uncertainty ΔV as well (L. P. Singer et al. 2016; W. Del Pozzo et al. 2018). GW detectors such as the LIGO, Virgo, and KAGRA detectors are designed to sense changes in the difference of the lengths of their orthogonal arms, ΔL = Δ(L1 − L2), caused by GWs, via laser interferometry. These �-shaped Michelson 21 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. interferometers measure the difference in phase of coherent light, split at a beam splitter located at the vertex of the �, after traversing the arms and recombining at the beam splitter Δf = 2πΔL/λ*, where λ* is the wavelength of the laser light (G. E. Moss et al. 1971; R. L. Forward 1978; R. Weiss 2022). For GW transients having durations much less than a day and wavelengths much greater than the length L of the detector arms, the strain induced on the arms is a linear combination of plus- and cross-polarizations of the metric perturbation (R. L. Forward 1978; V. N. Rudenko & M. V. Sazhin 1980; B. F. Schutz & M. Tinto 1987; K. S. Thorne 1987) h L L F h F h . 2( )= = ++ + × × Here F+ and F× are the detector’s beam pattern functions, which depend on the position on the sky from which the GW source is located, a polarization angle that defines the axes of the plus- and cross-polarization in the wave frame, the Earth rotation angle at the time of the signal’s arrival, and the location, orientation, and geometry of the detector on Earth’s surface (W. Anderson et al. 2001). Figure 4 shows the sky coordinate conventions used. For long-duration signals, effects of Earth’s rotation need to be included; for short-wavelength signals, the beam pattern functions also depend on the wavelength of the GWs (M. Rakhmanov et al. 2008; M. Rakhmanov 2009). Neither of these effects is significant in any of the transient signals detected to date. The amplitudes of the strains measured in a network of detectors provide additional information about the location of the source of the GW if the polarization of the GW is known owing to the dependence of the beam pattern functions on the position of the source on the sky (e.g., L. P. Singer & L. R. Price 2016). This information helps to break degeneracies in sky localiza- tion; for instance, with only two detectors, the source is typically localized to an extended arc or ring on the sky, but the amplitude response can help reduce this uncertainty to specific regions along that ring. Table 2 summarizes the parameters associated with a general transient plane GW, a detector’s response to such a GW, and the accuracy of localization of the wave’s source. LVK Catalog of Observed Transient GW Signals. In the companion article A. G. Abac et al. (2025b), we describe the significant transient GW candidates in GWTC-4.0, high- lighting those observed in O4a. GWTC-4.0 also provides the inferred properties of the GWs, as well as their sources, e.g., the masses and spins of the binary components under the assumption than the GWs were produced by CBCs. The GWTC dataset, along with other open data products, is detailed in the companion article A. G. Abac et al. (2025i). 5.1.2. Gravitational Lensing of GWs Like electromagnetic waves, GWs can be gravitationally lensed by massive objects, e.g., galaxies, interposed between the GW source and the observer. The GW polarization tensor is parallel propagated along geodesics (C. W. Misner et al. 1973) and is little affected by the gravitational potential of the lensing mass, so it is sufficient to consider scalar diffraction theory (R. Takahashi & T. Nakamura 2003). In a thin-lens approximation, the bending of the trajectory of the GW propagation occurs on a lens plane orthogonal to the line of sight and at the distance of the lensing body. With ξ1 and ξ2 as the coordinates of the lens plane, at each point on this plane there is an observed time delay T(ξ1, ξ2) relative to straight- line motion with no lens, corresponding to the path from the source to that point on the lens plane to the observer. This delay accounts for the gravitational field of the lens. GWs are deflected by a gravitational lens with the time delay field on the lens plane determining the complex phases of the interfering partial waves used to compute a frequency- dependent complex-valued magnification factor. This factor is given by the Fresnel–Kirchhoff diffraction formula F f i D D D z f c ifT d d 1 exp 2 , , 3 OS OL LS L 1 2 1 2 ( ) ( ) [ ( )] ( ) = + × where the integral is over the lens plane, f is the observed GW frequency, (1 + zL)f is the blueshifted frequency of the GW on the lens plane (zL is the redshift of the lens), and the distances DOS, DOL, and DLS are the distances between the observer (us) and the GW source, between the observer and the gravitational lensing object, and between the lensing object and the source, respectively (P. Schneider et al. 1992). In a cosmological setting, these are angular diameter distances (D. W. Hogg 1999). The geometric optics limit corresponds to Fermat’s principle, in which the geodesic paths taken by GWs are those passing through the lens plane at extrema of this two- dimensional time delay field T(ξ1, ξ2), which may be local minima, which produce Type I images, local maxima, which produce Type III images, or saddle points, which produce Type X NCP N ψ α −δ source GST GHA equatorial plane wave plane prim e m e rid ia n ♈ Figure 4. Relationship between the sky location in equatorial coordinates, the polarization angle, and the GW coordinate frame. The direction from the source to Earth is N, and the vector X defines a reference direction on the transverse plane called the wave plane. The location of the source on the sky in the equatorial coordinate system is given by its R.A. α and decl. δ. The polarization angle ψ is the angle counterclockwise about N between the equatorial plane and X. Also shown is the Greenwich sidereal time (GST), the angle between the first point of Aries and the prime meridian, and the Greenwich hour angle (GHA) of the source, GHA = GST − α. NCP is the north celestial pole. 22 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. II images (P. Schneider et al. 1992). Equation (3) is evaluated in this high-frequency limit by use of the stationary phase approximation to obtain F f i f t i nexp 2 , 4j j j j( ) ( ) ( )µ± = ± where jµ and tj are the magnification amplitude and observed time delay of image j, and nj is 0, 1/2, or 1 for Type I, Type II, and Type III images, respectively. Therefore, such images are magnified or demagnified by a factor that is positive for Type I images and negative for Type III images, while the gravita- tional waveform of Type II images is additionally distorted, appearing as the Hilbert transform of the original waveform (L. Dai & T. Venumadhav 2017; J. M. Ezquiaga et al. 2021). For GW transients, the images are a set of repeated signals from the same event observed at different times, with the delays determined by the differences in the time delay field on the lens plane of the different images. These delays are typically minutes to months for galaxy lenses (S.-S. Li et al. 2018; K. K. Y. Ng et al. 2018; M. Oguri 2018) and up to years for galaxy cluster lenses (G. P. Smith et al. 2017, 2018; A. Robertson et al. 2020; D. Ryczanowski et al. 2020). The images also appear at different points on the sky, with arcminute-scale separation, but GW detectors have insufficient sky localization capabilities to distinguish them in this way. When gravitational lensing can be described in this geometric optics limit, it is referred to as strong lensing. However, when the wavelength of the GW is comparable to the Schwarzschild radius of the gravitational lens, the geometric optics limit of Fermat’s principle is no longer valid, and the Fresnel–Kirchhoff diffraction formula of Equation (3) must be used to determine the complex-valued and frequency- dependent magnification factor. Such lensing effects can result from objects having masses up to 105M⊙, and searches can be done in a modeled (e.g., M. Wright & M. Hendry 2021) or phenomenological (A. Liu et al. 2023) way. Searches for Gravitational Lensing Signatures in GW Signals. In the companion article A. G. Abac et al. (2025h), we present searches for gravitational lensing signatures in GWTC-4.0. Such signatures sought include multiple images from strong lensing, individual Type II strongly lensed images, and waveform distortions induced by point-mass lensing. 5.1.3. GW Polarization and Propagation in Alternative Theories of Gravity In GR, plane GW perturbations to flat spacetime propagate at the speed of light and contain two transverse polarizations. However, in modified theories of gravity extending beyond GR, additional polarizations may be present, including two transverse-longitudinal spin-1 vector modes, a transverse spin- 0 scalar mode, and a longitudinal spin-0 scalar mode (D. M. Eardley et al. 1973a, 1973b; C. M. Will 2018). With multiple detectors, it is possible to test for such additional polarizations (B. F. Schutz 1986). A linear combination of strain data from three detectors can be formed in which any GW signal from a known sky location and containing only plus- and cross-polarizations is canceled (Y. Guersel & M. Tinto 1989; S. Klimenko et al. 2008; P. J. Sutton et al. 2010; J. D. E. Creighton & W. G. Anderson 2011; I. C. F. Wong et al. 2021). Any residual GW signal found in such a null space would provide evidence for the presence of vector or scalar non-GR polarizations. In addition, in alternative Lorentz invariance violating theories of gravity or in which the graviton is massive, GWs are dispersive. Certain theories of dark energy also result in dispersive GW propagation (C. de Rham & S. Melville 2018; T. Baker et al. 2022; I. Harry & J. Noller 2022). The GW dispersion relation between the frequency f and the wavelength λ (one where they are not inversely proportional) leads to phase speeds and/or group speeds that differ from the speed of light. Such propagation effects can be measured for a known waveform by the anomalous arrival times of different frequency components. A common parameterized dispersion Table 2 Parameters Describing a Transient Plane GW, a Detector’s Instantaneous Antenna Response in the Long-wavelength Limit, and Measures of Inferred Localization of the Signal on the Sky Parameter Name Symbol Notes [Dimensions] Plus- and cross-polarizations h+, h× Functions describing the plus-polarization (h+) and cross-polarization (h×) of the metric perturbation [dimensionless] Geocentric arrival time tgeo Time of arrival at the center of Earth of some fiducial point in the GW’s waveform, normally close to the peak amplitude of the waveform [time] Propagation direction N Direction of propagation of the GW, the unit vector normal to the planar wavefronts; the direction to the source of the wave is −N [dimensionless] Right ascension (R.A.) α Azimuth of the sky location of the source of the GW in the equatorial coordinate system (see Figure 4) [angle] Declination (decl.) δ Latitude of the sky location of the source of the GW in the equatorial coordinate system (see Figure 4) [angle] Polarization angle ψ Orientation of the axes defining the plus- and cross-polarization on the transverse plane of the GW relative to the line of nodes of this plane and Earth’s equatorial plane (see Figure 4) [angle] Plus and cross beam patterns F+, F× Antenna response of a detector to the plus-polarization (F+) and the cross-polarization (F×), functions of the sky location of the source, the polarization angle, the geocentric arrival time of the signal, and the location, orientation, and geometry of the detector on Earth (W. Anderson et al. 2001) [dimensionless] Detector strain h GW-induced strain on a detector, Equation (2); the GW readout of the detector is proportional to this quantity [length/ length] Sky area ΔΩ Localization area, typically taken as the 90% credible area; if results at different CLs are quoted, these are indicated with a subscript, e.g., ΔΩ50 is the 50% credible area [solid angle] Volume localization ΔV Localization volume (for signals where the distance to the source can be estimated), typically taken as the 90% credible volume; if results at different CLs are quoted, these are indicated with a subscript, e.g., ΔV50 is the 50% credible volume [volume] 23 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. relationship is motivated by a modified energy–momentum relationship for the graviton of the form (S. Mirshekari et al. 2012) E pc A pc , 52 2( ) ( ) ( )= + where Aα is a GR-violating parameter having dimensions of (energy)2−α. For de Broglie waves, E = 2πℏf and p = 2πℏ/λ, where 2πℏ is the Planck constant. Such a modified energy– momentum relation leads to a dispersion relation in which the phase velocity vp is given by v c A c 1 2 , 6 p 2 2 ( )= + where the phase velocity is related to the frequency and the wavelength of the GW, vp = λf. The group velocity, v v dv d lng p p/= , determines the difference in arrival times of different frequency components of the GW after propaga- tion from its source to the observer. For small deviations from GR (vp ≈ c), the group velocity is frequency dependent with v c c A f 1 2 1 2 . 7 g 2( ) ( ) ( ) Special cases include (i) a graviton of mass mg ≠ 0 for which α = 0, A m cg0 2 4= , and v c c f c 1 2 , 8gg 2 ( ) where λg = 2πℏ/(mgc) is the Compton wavelength of the graviton, and (ii) the case in which GWs are nondispersive but propagate at a speed different from the speed of light for which α = 2 and v c A1 . 9g 2 ( )= + Stringent bounds on the latter are provided by the close temporal association of the BNS signal GW170817 and the gamma-ray burst GRB 170817A (the gamma rays arriving less than 2 s after the BNS GW merger signal), resulting in |A2| ≲ 10−14 (B. P. Abbott et al. 2017f). The Einstein–Hilbert action of GR contains second derivatives of the spacetime metric (S. Weinberg 1972; C. W. Misner et al. 1973; R. M. Wald 1984; S. M. Carroll 2019). Standard model extensions having modified actions containing third derivatives of the metric can produce CPT- violating terms in the gravitational field equations, which can produce birefringence effects in which different GW helicities propagate with different phase velocities (V. A. Kostelecky 2004; V. A. Kostelecký & M. Mewes 2016; M. Mewes 2019; L. Haegel et al. 2023). Other theories of gravitation also have GWs with birefringent propagation (T. Zhu et al. 2024). Such birefringence leads to a frequency-dependent rotation of the GW polarization angle. Both GW birefringence and the modified GW dispersion relation can potentially be anisotropic, where the magnitude of the observed effect depends on the direction to the source. Tests of GR: GW Polarization and Propagation. In the companion article A. G. Abac et al. (2025d), we test the GR prediction of the polarizations of GWs by searching for evidence of vector- or scalar-polarization modes in observed GW signals. Meanwhile, A. G. Abac et al. (2025e) present tests of a modified dispersion relation and of anisotropic birefringence using GW signals from CBCs, for which it is assumed that the GW near the source is described by GR to a good approximation, but the waveform is affected during propagation. 5.2. Compact Binary Coalescence Binaries consisting of two BHs (BBH systems), consisting of two NSs (BNS systems), or in which one component is an NS and the other a BH (NSBH systems), have all been observed by the LVK (B. P. Abbott et al. 2016a, 2017a; R. Abbott et al. 2021c). The detectable signal produced by such systems arises from the late stage of orbital decay, driven by GW emission, and by the ensuing merger of the binary components and the settling of the resulting object (an NS or BH) to a final, stationary configuration (K. Chatziioannou et al. 2024). Table 3 provides a list of parameters used to describe CBCs. 5.2.1. Newtonian Inspiral At early stages of the inspiral, when the magnitude of the difference in velocity vectors of the two components of the binary, v, is much smaller than the speed of light, the orbit is determined approximately by Newtonian mechanics, while the gravitational radiation is described by the quadrupole formula (A. Einstein 1916, corrected by A. S. Eddington 1922, page 279). For a quasi-circular orbit that is inclined an angle ι relative to the direction to an observer, h+ and h× are sinusoidal and are 90° out of phase, h GM c r v c 2 1 cos cos 2 10a2 2 2 ( ) ( )= ++ and h GM c r v c 4 cos sin 2 , 10b 2 2 ( )=× where r is the distance between the source and the observer, M = m1 + m2 is the total mass of the system, η = m1m2/M 2 is the symmetric mass ratio, Mη is the reduced mass of the system, and f is the orbital phase relative to the ascending node (P. C. Peters & J. Mathews 1963; K. S. Thorne 1987; L. S. Finn & D. F. Chernoff 1993; C. M. Will & A. G. Wiseman 1996). See Figure 5. When ι = 0 or ι = π (face-on and face-off, respectively), the amplitudes of the sinusoidal functions h+ and h× are equal and the GW is circularly polarized; when ι = π/2 (edge-on), h× = 0 and the GW is linearly polarized. The GW luminosity of such a system, i.e., the power in gravitational radiation, is E c G v c 32 5 . 11GW 5 2 10 ( )= This radiation gives rise to a secular orbital decay. Since the (Newtonian) energy of the bound system is Eorb = − (1/2)ηMv2, and equating E EGW orb= , we deduce that the period of the orbit, P = 2πGM/v3 by Kepler’s third law, evolves according to P v c 192 5 . 12 5 ( )= At fixed orbital period (or orbital frequency), the orbital velocity is proportional to the cube root of the total mass, 24 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. v ∝ M1/3. It can be seen, then, that h+, h× ∝ ηM5/3, E MGW 5 3 2( )/ , Eorb ∝ ηM5/3, and P M5 3/ . At the Newtonian level of approximation, a single combination of the component masses, M M m m m m , 133 5 1 2 3 5 1 2 1 5 ( ) ( ) ( )/ / / = = + known as the chirp mass, solely determines both the amplitude of a GW at fixed orbital frequency and its frequency evolution (P. Kafka 1988; C. Cutler et al. 1993; L. S. Finn & D. F. Chernoff 1993). This chirp mass is normally the most accurately measured mass parameter for low-mass systems in which most of the signal observed arises from the pre-merger phase. Table 3 Parameters Describing a CBC System with Quasi-circular Orbits Parameter Name Symbol Notes [Dimensions] Primary and secondary masses m1, m2 Mass of the more massive (m1) and less massive (m2) body in the system, m1 � m2 [mass] Chirp mass M See Equation (13) [mass] Total mass M M = m1 + m2 [mass] Final mass Mf Mass of the remnant [mass] Mass ratio q q = m2/m1 � 1 [dimensionless] Symmetric mass ratio η m m m m 1 41 2 1 2 2( )/ /= + [dimensionless] Energy radiated Erad Erad = (M − Mf)c2 [energy] Peak luminosity ℓpeak Peak GW luminosity, typically 0.1% of the Planck luminosity (ℓPlanck = c5/G) for BBH coalescences [power] Primary and secondary spin vectors S1, S2 Spin angular momentum of the primary (S1) and secondary (S2) [angular momentum] Primary and secondary dimensionless spin magnitudes χ1, χ2 Sc Gm1,2 1,2 1,2 2( )/= ; χ1,2 � 1 for Kerr BHs primary/secondary [dimensionless] Remnant dimensionless spin magnitude χf cS GMf f f 2( )/= where Sf is the magnitude of the remnant’s spin angular momentum; χf � 1 for a Kerr BH remnant [dimensionless] Newtonian orbital angular momentum L Instantaneous orbital angular momentum about the center of mass; defines z-direction for spin coordinates [angular momentum] Total angular momentum J J = L + S1 + S2 [angular momentum] Primary and secondary tilt angle θ1, θ2 Angle between S1,2 and L [angle] Spin azimuthal angle difference f12 Angle measured clockwise about L from L × (S1 × L) to L × (S2 × L) [angle] Effective inspiral spin parameter χeff See Equation (15) [dimensionless] Effective precession spin parameter χp See Equation (16) [dimensionless] Orbital inclination angle ι Angle between L and the direction to Earth N (see Figure 5) [angle] Source inclination angle θJN Angle between J and the direction to Earth N [angle] Viewing angle Θ min ,JN JN{ }= [angle] Orbital phase f Phase of a binary’s orbit, the angle on the orbital plane between the separation vector (the position vector of the primary minus the position vector of the secondary) and the line of nodes, L × N (see Figure 5) [angle] Coalescence phase fc Orbital phase, the angle on the orbital plane between the separation vector (the position vector of the primary minus the position vector of the secondary) and the line of nodes, L × N, at a point in the evolution corresponding to the point in the waveform used to define tgeo (see Table 2) [angle] Angular diameter distance DA An object of transverse length x is observed to subtend an angle in radians of x/DA when both the object and observer are at rest relative to a homogeneous cosmology (D. W. Hogg 1999) [length] Transverse comoving distance DM Areal radius of a sphere centered on a point in an isotropic cosmology, defined so the sphere has area D4 M 2 (D. W. Hogg 1999) [length] Luminosity distance DL A source of isotropic radiation having luminosity ℓiso is observed to have flux D4iso L 2( )/ when both the source and observer are at rest relative to a homogeneous cosmology (D. W. Hogg 1999) [length] Redshift z The fractional difference between the frequency of a wave at emission at its source fsrc and its observed frequency at a detector fdet , z f f fsrc det det( )/= ; the reference cosmology for the relationship between distance and the cosmological redshift is given in the text [dimensionless] Primary and secondary dimensionless tidal deformabilities Λ1, Λ2 See Equation (18); Λ1,2 = 0 for a BH primary/secondary [dimensionless] Effective tidal deformability ˜ See Equation (19); 0˜ = for a BBH [dimensionless] Primary and secondary dimensionless spin- induced quadrupole moments κ1, κ2 See Equation (21); κ1,2 = 1 for a BH primary/secondary [dimensionless] Primary and secondary radii R1, R2 Areal radii of primary and secondary objects, defined so their surface areas are R4 1,2 2 ; used in defining NS compactness [length] Primary and secondary compactness C1, C2 Dimensionless mass-to-radius ratios C1,2 = Gm1/(c2R1,2) of primary/secondary; C1 1 11,2 1,2 2/ = + + for Kerr BH primary/secondary [dimensionless] Merger rate density R Rate of binary mergers per unit volume in the local Universe; may be expressed as a function of cosmological redshift, R z( ); the rate in the local Universe R z 0( )= can be notated R0; subscripts can be used if considering different populations, e.g.,R BNS ,R NSBH , andR BBH [time−1 volume−1] 25 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. 5.2.2. Post-Newtonian Inspiral and Other Effects Additional terms in the GW amplitude and frequency evolution appear at higher orders in v / c in a post-Newtonian (PN) expansion in the equations of motion and in the gravitational emission (L. Blanchet 2014). At the Newtonian order, the frequency of the GW is twice the frequency of the orbital motion, f = 2forb = 2/P, and v GMf . 143 ( )= At O(v/c) beyond this, additional components to the GW at frequencies at one and three times the orbital frequency arise from current quadrupole and mass octupole radiation, and other components occur at O(v2/c2) beyond Newtonian order from current octupole and mass hexadecapole radiation (K. S. Thorne 1980); the amplitudes of these higher-order multipole moments of radiation are proportional to a different combination of component masses (L. E. Kidder 2008). The frequency evolution also gains additional terms at O(v2/c2) beyond the leading-order Newtonian term, again having a different dependence on the component masses from the leading Newtonian order (R. V. Wagoner & C. M. Will 1976). Spin effects from rotating binary components also appear in PN corrections to the quadrupole waveform due to O(v3/c3) spin–orbit and O(v4/c4) spin–spin effects (L. E. Kidder et al. 1993) and to precession of the orbital plane if the spin angular momentum vectors of the bodies are not aligned (or antialigned) with the orbital angular momentum vector (T. A. Apostolatos et al. 1994). The dimensionless parameter χeff, defined as L S S L c GM m m , 15eff 1 1 2 2· ( ) ( )/ / = + where S1 and S2 are the spins of the two binary components and L is the orbital angular momentum about the center of mass, is an effective inspiral spin parameter that is conserved under the orbit-averaged precession equations of motion at O(v4/c4) (T. Damour 2001; E. Racine 2008; M. Kesden et al. 2010; L. Santamaria et al. 2010; P. Ajith et al. 2011). Whereas χeff depends on the spin components aligned with the orbital angular momentum, a dimensionless effective precession spin parameter that depends on in-orbital-plane components of the spins, L S L L S L c Gm m m m m m m max , 3 4 3 4 , 16 p 1 1 1 1 2 2 1 2 2 {| | | | | | | | ( ) / / = × + + × captures the dominant precession effects (P. Schmidt et al. 2015). Deformable binary components (NSs but not BHs) suffer an induced quadrupole deformation Qij under an external tidal field Eij, where these quadrupole tensors are those appearing in a multipole expansion of the Newtonian potential centered on the body of mass m as (K. S. Thorne 1998) E x x x x Gm GQ x x x x 1 2 3 1 2 . 17 ij i j ij ij i j 2 5 ( ) ( ) = + + The dimensionless tidal deformability, Λ, of a body of mass m is defined in terms of the ratio of the induced deformation to the external tidal field as E GQ Gm c , 18 ij ij2 5( ) ( ) / = where BHs have Λ = 0. Newtonian tidal interactions of deformable components appear as effective O(v10/c10) correc- tions to the binding energy and GW luminosity (E. E. Flanagan & T. Hinderer 2008). At this order, the dimensionless combination of tidal parameters given by (M. Favata 2014) m m m m m m m m 16 13 12 12 191 2 1 4 1 2 1 2 4 2 1 2 5 ˜ ( ) ( ) ( ) ( )= + + + + appears, where Λ1 and Λ2 are the dimensionless tidal deformabilities of the two bodies, and it is this parameter that is most measurable in the waveforms produced by binaries with deformable companions (E. Poisson 2021). Spinning bodies experience quadrupole deformation of the form Q Q Q Qdiag 1 3 , 1 3 , 2 3 , 20ij ( )= where Q is the spin-induced mass quadrupole moment scalar. The quadrupole deformations induced by an object’s spin result in Newtonian quadrupole–monopole effects as an effective O(v4/c4) correction, the same order as the spin–spin coupling relativistic effects (E. Poisson 1998). The size of the Ω ω rp  L N X plane of sky orbital p lane ι φ Figure 5. Relationship between the orbital elements and the GW coordinate frame. The direction from the source to Earth is N, and the vector X defines a reference direction on the transverse plane (the plane of the sky). The inclination ι is the angle between N and the orbital angular momentum vector L. The longitude of the ascending node of the orbit Ω is the angle on the plane of the sky between X and the ascending node ♌, N × L. The angle Ω is degenerate with the polarization angle ψ. The orbit of the primary about the center of mass of the system is shown. The orbital phase f is the angle on the orbital plane between the ascending node and position vector of the primary relative to the center of mass. For an eccentric orbit, the distance of the primary from the center of mass at periapsis is rp, and the argument of the periapsis ω for the primary is the angle on the orbital plane between the ascending node and the position vector of the primary at periapsis. 26 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. spin-induced deformation depends on the nature of the body, where the ratio of the quadrupole scalar to the square of the body’s spin magnitude is given by the dimensionless parameter κ as S Q mc , 21 2 2 ( )= where m is the mass of the body. For a BH, κ = 1 (K. S. Thorne 1980). Binaries detected by ground-based observatories are com- monly assumed to have negligibly small orbital eccentricity remaining by the time the orbital period has decayed to the point that the GW frequencies have entered the high-frequency sensitivity band of the detectors. This decay in eccentricity happens because orbital eccentricity is efficiently reduced by GW emission during the orbital decay (P. C. Peters 1964). However, there are channels of compact binary formation that could result in nonnegligible orbital eccentricity being present even at the last stages of inspiral observed by ground-based detectors (e.g., M. Mapelli 2020). The leading-order effects of orbital eccentricity would appear at the Newtonian level (P. C. Peters & J. Mathews 1963). Two additional parameters are needed to describe an eccentric binary system, the eccentricity e and the argument of the periapsis ω. Although these are well-defined for Newtonian two-body systems, there are different ways to generalize their definitions for relativistic systems, and there is not yet a settled convention for these parameters (M. A. Shaikh et al. 2023). Tests of GR from CBC Inspiral. PN theory in GR predicts the relative amplitudes of subdominant modes of GW radiation (L. Blanchet 2014), which depend on the binary’s masses and spins (e.g., K. G. Arun et al. 2009). Thus, allowing for freedom in these amplitudes and checking whether they are consistent with those predicted by GR provides a consistency test of the agreement of the signal with the waveform model used to analyze it (A. Puecher et al. 2022). In the companion article A. G. Abac et al. (2025d), this test is carried out for BBH signals, considering deviations, δAℓm, in the amplitude of the (ℓ = 2, m = ± 1) or (ℓ = 3, m = ± 3) subdominant multipole moments relative to the dominant (ℓ = 2, m = ± 2) and other multipole moments. The PN expansion of the orbital energy and GW energy loss makes a prediction of how the GW phase evolves with time as the orbit decays (L. Blanchet 2014). The PN formalism expresses this phase evolution with a set of coefficients in a series expansion of the GW phase in terms of powers (v/c)n−5 and v c v clogn 5( ) ( )/ / for integer n (with n = 0 for the leading- order Newtonian inspiral) that depend on the binary compo- nents’ masses and spins for point particles. Violations of GR can lead to differences in the values of the PN coefficients from those predicted by GR (e.g., N. Yunes & F. Pretorius 2009; S. Tahura & K. Yagi 2018), which could be observed in a GW signal (L. Blanchet & B. S. Sathyaprakash 1994, 1995; K. G. Arun et al. 2006; C. K. Mishra et al. 2010; T. G. F. Li et al. 2012). In the companion article A. G. Abac et al. (2025e), we present parameterized tests for such violations. Effects arising from the finite size of the component masses of a binary include spin-induced multipole moments, most importantly their spin-induced quadrupole moments Q, which also affect the orbital evolution. For a BH, there is a fixed relation between its spin-induced quadrupole moment and its mass and spin (E. Poisson 1998). Deviations from this predicted value, as observed in the phase evolution of a GW signal, can be used to distinguish a BBH from a compact binary containing exotic, non-BH components. Some examples of exotic alternatives to BHs, being compact objects capable of having masses greater than the maximum mass of an NS, include boson stars (D. J. Kaup 1968; R. Ruffini & S. Bonazzola 1969), gravastars (P. O. Mazur & E. Mottola 2004), fuzzballs (S. D. Mathur 2005), and firewalls (A. Almheiri et al. 2013). The companion article A. G. Abac et al. (2025e) presents such parameterized tests of the nature of the components of CBCs. 5.2.3. Compact Binary Merger and Ringdown The final stages of GW emission from CBCs that result in a BH remnant can be modeled as a linear gravitational perturbation to a Kerr BH spacetime (W. H. Press & S. A. Teukolsky 1973). Remarkably, the partial differential equations for the outgoing GW content of such a perturbation decouple from the other gravitational modes, and those decoupled equations are separable into a radial equation, an angular equation, and an exponential function of time with a complex frequency (S. A. Teukolsky 1972, 1973). The separation results in a spectrum of complex eigenfrequencies of the GW perturbations to the BH spacetime indexed by integer degree ℓ and order m numbers, ℓ � 2 and |m|� ℓ, and integer overtone n with n � 1 (E. W. Leaver 1985; E. Berti et al. 2006). The angular eigenfunctions, which depend on ℓ and m, also depend on the dimensionless complex frequency and the dimensionless spin parameter of the remnant BH. The complex eigenfrequencies describe the spectrum of exponen- tially decaying sinusoidal GW quasi-normal modes that make up what is called the BH ringdown. GR therefore provides a prediction for the relationship between the frequency and the decay constant for the spectrum of such quasi-normal modes that depend solely on the mass and spin of the final BH, and thus the BH ringdown radiation can be used to test these predictions of GR. Spanning the region between the portion of the waveform that can be computed by PN calculations at early time and the portion that can be computed by a superposition of quasi- normal modes at late time is what is known as the merger phase of the compact binary. Due to the nonperturbative nature of this phase, numerical relativity (NR) solutions to Einstein’s field equations are sought (L. Lehner & F. Pretorius 2014; M. D. Duez & Y. Zlochower 2019). Such solutions both interpolate these early and late phases and also provide the information about the quasi-normal mode amplitudes and phases excited, as well as the mass and spin of the remnant BH (F. Hofmann et al. 2016; J. Healy & C. O. Lousto 2017; X. Jiménez-Forteza et al. 2017). When at least one component of the binary in the CBC is not a BH (i.e., an NS), the merger and ringdown phases might be considerably more complex owing to the presence of matter in the system. NR is typically required to compute the entire post- inspiral phase of the GWs emitted from such systems (J. A. Faber & F. A. Rasio 2012; K. Kyutoku et al. 2021). One important piece of such simulations is to determine whether disruption of an NS component occurs, particularly in the case of NSBH systems in which the NS might be swallowed whole by the BH (typical for high-mass and low- spin BHs) or might be tidally disrupted by the BH (typical for low-mass or high-spin BHs). Such NS disruption would be expected to produce electromagnetic emission that could be 27 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. observed by electromagnetic astronomical observatories. Guided by numerical simulations, one can estimate whether a system having particular parameters inferred from the inspiral phase will be electromagnetically bright and so a candidate for electromagnetic follow-up observations (F. Foucart et al. 2018; D. Chatterjee et al. 2020; M. Berbel et al. 2024). Depending on the masses of the initial components, the product of the merger of two NSs might be another NS, a supramassive NS (a uniformly spinning NS that is more massive than the highest allowed mass for a nonspinning NS, which remains an NS until its angular momentum is dissipated, resulting in its collapse to a BH), a hypermassive NS (an NS more massive than would be allowed for any stationary, spinning configuration, but which is temporarily supported by differential rotation, and which will ultimately collapse to a BH), or there might be a direct collapse on a dynamical timescale to form a BH after the merger (T. W. Baumgarte et al. 2000; A. L. Piro et al. 2017). Both the electromagnetic emission and GW emission from these different scenarios are expected to vary considerably (B. P. Abbott et al. 2017c). Tests of GR from CBC Merger. NR simulations of BBHs in GR provide predictions for the GW waveform spanning the inspiral, merger, and final ringdown phases of evolution. Tests for violations of GR can be performed by subtracting the best- fit GR waveform from the observed data and testing whether the remaining residual is consistent with detector noise or whether there is remaining signal present. Alternatively, since NR predicts how a final BH mass and spin are related to the initial BH masses and spins for a BBH CBC (F. Hofmann et al. 2016; J. Healy & C. O. Lousto 2017; X. Jiménez-Forteza et al. 2017), a test of consistency between the initial orbital parameters and the final BH mass and spin can be performed. Here the initial component BH masses and spins can be determined from the early inspiral phase of the GW signal, while the mass and spin of the final BH are found from the late-time ringdown radiation. In practice, such a consistency test divides the GW signal into low- and high-frequency portions (below and above a given cutoff frequency) that are independently modeled with full inspiral–merger–ringdown waveforms (A. Ghosh et al. 2016, 2018). Companion article A. G. Abac et al. (2025d) presents results from such residual and inspiral–merger–ringdown consistency tests. In GR, a BH remnant produced by a CBC will rapidly settle to a stationary Kerr BH (R. P. Kerr 1963), uniquely characterized by its mass and spin (W. Israel 1967; B. Carter 1971), through emission of ringdown radiation in a spectrum of quasi-normal modes, as described earlier. These quasi-normal modes have a discrete spectrum of complex- valued eigenfrequencies (the imaginary part of which determines the decay timescale), so a possible non-BH remnant (e.g., C. F. B. Macedo et al. 2013), or modifications of the spectrum in alternative theories of GR (e.g., P. A. Cano et al. 2024), can be tested by looking for deviations in the observed ringdown radiation from the anticipated spectrum of quasi-normal modes (E. Berti et al. 2025). Furthermore, if the remnant object does not possess an event horizon, ingoing GW radiation can be reflected off of a surface or scattered off of an inner potential and reemerge as an echo signal observed within ∼seconds after the merger (V. Cardoso et al. 2016; V. Cardoso & P. Pani 2019; N. Siemonsen 2024). The companion article A. G. Abac et al. (2025f) presents tests of the nature of the remnant resulting from CBC through observed quasi-normal mode spectra and searches for GW echoes. The post-inspiral portion of a BBH signal can be phenomenologically modeled with various parameters that are fitted to NR simulations (G. Pratten et al. 2020). The companion article A. G. Abac et al. (2025e) explores possible deviations of these parameters from their nominal values (J. Meidam et al. 2018; S. Roy et al. 2025). 5.2.4. Redshift and Cosmological Effects GWs can be redshifted, just as electromagnetic waves are. These changes are caused by the Doppler effect due to relative motion of the emitter and the observer (often described in terms of peculiar velocities relative to the rest frame of the cosmological microwave background radiation), due to the expansion of space between the emitter and the observer, or due to gravitational redshift if the emitter and observer have different gravitational potentials. For sources beyond the nearby Universe (having redshifts ≳0.1), cosmological expansion is the dominant source of redshift (E. R. Peterson et al. 2022). The redshift is the fractional difference between the frequency of a wave at emission at its source fsrc, and its observed frequency at a detector fdet, z = ( fsrc − fdet)/fdet (D. W. Hogg 1999). Thus, the observed frequency of a wave is related to its emitted frequency by fdet = fsrc/(1 + z). Similarly, an interval in time in the source-frame dtsrc is related to an observed interval in time by a detector dtdet by dtdet = (1 + z)dtsrc. Equations (10) and (12) are both parameterized in terms of the orbital velocity v, which is related to the GW frequency f in the dominant mode by Equation (14). At a fixed moment in a GW waveform, where the binary has some instantaneous value of v, we have v GMf GM z f1 . 223 src det( ) ( )= = + That is, a redshifted signal, observed at frequency fdet, produced by a system with intrinsic mass M has identical morphology to an unredshifted signal produced by a system with intrinsic mass (1 + z)M (A. Krolak & B. F. Schutz 1987). If the redshift is unknown, then the observable mass parameters are the various combinations of (1 + z)m1 and (1 + z)m2, e.g., Mz1( )+ and (1 + z)M. These mass parameters with the 1 + z scale factor are referred to as detector-frame masses, m z m11 det 1( )= + , m z m12 det 2( )= + , Mdet = (1 + z)M, and M Mz1det ( )= + . PN corrections to the waveform preserve this degeneracy for point particles (and BHs). However, for NSs, a functional relationship between the mass of an NS and its tidal deformability means that a measurement of ˜ can break the degeneracy between mass and redshift, allowing the two to be independently measured (C. Messenger & J. Read 2012). The amplitudes of h+ and h× given in Equation (10) also depend on the total mass through the factor M/r. If the factor (1 + z)M is determinable from the rate of decay of the orbital period, Equation (12), then the amplitude factor can be written as [(1 + z)M]/[(1 + z)r], suggesting that the measurable amplitude distance parameter is (1 + z)r. The parameter r that appears in inverse proportion to the GW amplitude in Equation (10) represents the areal radius, 28 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. i.e., spheres centered on the GW source have area 4πr2. Within a cosmological setting, this parameter is the transverse comoving distance DM (D. W. Hogg 1999). Then, if the redshift is entirely due to the cosmological expansion of spacetime, the combination (1 + z)DM is equal to the luminosity distance of the source, and this becomes the observable distance parameter from the GW amplitude. In this sense, then, given a known cosmology (i.e., the values of the Hubble constant, matter density, and the spatial curvature), the functional relationship between luminosity distance and redshift allows the determination of the latter from the former, and the intrinsic masses, e.g., M, can then be deduced from the observed mass–redshift combined para- meters, e.g., Mdet = (1 + z)M. However, if other redshift effects are present, e.g., due to peculiar motion of the source or the observer relative to the Hubble flow, the combination (1 + z)DM is no longer equal to the luminosity distance. Nevertheless, when reporting the parameters of a CBC, we normally assume that cosmological expansion is the only significant source of redshift, and so the observed amplitude parameter (1 + z)DM is referred to as luminosity distance DL, while a dimensionful intrinsic mass parameter such as the primary mass m1 is derived from observed detector-frame mass parameters as m m z D11 1 det L[ ( )]/= + , where the relationship between the redshift and the luminosity distance, z(DL), is obtained by some standard cosmological model. The only case where this was not done was for GW170817, where the measured geocentric redshift to its host galaxy NGC 4993 was used (B. P. Abbott et al. 2019b). The main uncertainty in the chirp mass of the system comes from the unknown peculiar velocity of the system relative to its host galaxy. Unless otherwise specified, the reference cosmology used to relate luminosity distance to redshift throughout the works is a ΛCDM model (P. J. E. Peebles & B. Ratra 2003) corresp- onding to a spatially flat Friedman–Lemaître–Robertson– Walker spacetime (G. Lemaitre 1931; H. P. Robertson 1935a, 1935b, 1936; A. G. Walker 1937; S. Weinberg 1972; C. W. Misner et al. 1973; A. Friedmann 1999b, 1999a) with Hubble constant H0 = 67.9 km s−1 Mpc−1, matter density parameter Ωm = 0.3065, and cosmological constant density parameter ΩΛ = 1 − Ωm = 0.6935 (P. A. R. Ade et al. 2016, column TT+lowP+lensing+ext of Table 4). Constraints on Cosmic Expansion from GW Observations. If the redshift of a GW source can be determined indepen- dently of its distance, then a distance–redshift relationship can be obtained and used to infer cosmological parameters (B. F. Schutz 1986; A. Krolak & B. F. Schutz 1987). Here the CBC is called a standard siren (akin to the standard candles such as Cepheid variables and Type Ia supernovae used to measure distances to their galaxy hosts), where the luminosity distance of the CBC is inferred from the amplitude of the GWs (D. E. Holz & S. A. Hughes 2005). The most direct method of determining the redshift of a GW source is if there is an electromagnetic counterpart in which spectroscopic measurements of the redshift of its host galaxy can be made (A. Krolak & B. F. Schutz 1987; D. E. Holz & S. A. Hughes 2005; N. Dalal et al. 2006; H.-Y. Chen et al. 2018). This method is known as the bright siren method. For example, the BNS coalescence GW170817 (B. P. Abbott et al. 2017a) was associated with the optical kilonova AT 2017gfo in the galaxy NGC 4993 (B. P. Abbott et al. 2017b), which allowed for a measurement of the maximum a posteriori value of the Hubble constant with 68.3% credible level (CL) highest-density interval 69 km s Mpc8 17 1 1+ (B. P. Abbott et al. 2021a). If no electromagnetic counterpart to a GW is observed, various methods are available to deduce the associated redshift (BBHs are not normally expected to produce any electro- magnetic radiation, unless there is matter present in their environment). One such method, the galaxy catalog method, also called the dark siren method, is to obtain statistical association of GW sources with potential host galaxies observed in surveys (B. F. Schutz 1986; C. L. MacLeod & C. J. Hogan 2008). This is usually done simultaneously with information obtained from another method, the spectral siren method. In the spectral siren method, a known feature in the mass distribution of the population of CBCs is used to statistically infer the redshift of a number of sources at a given distance by how the observed detector-frame mass distribution is shifted with respect to the local (zero-redshift) distribution (D. F. Chernoff & L. S. Finn 1993; S. R. Taylor et al. 2012; W. M. Farr et al. 2019; S. Mastrogiovanni et al. 2021). Finally, future observations of BNS mergers may be capable of directly inferring the redshift of the source from the GW signal alone through measurements of the NS tidal deformations (C. Messenger & J. Read 2012; D. Chatterjee et al. 2021). The companion article A. G. Abac et al. (2025g) reports on constraints on the cosmic expansion history based on combined CBC bright and dark sirens, including both the galaxy catalog method and the spectral siren approach. If GWs propagate through cosmological backgrounds differently from electro- magnetic waves in a manner that produces a different distance– amplitude relation, the modified propagation effects can be observed using standard siren methods (E. Belgacem et al. 2018). The companion article A. G. Abac et al. (2025g) also reports on constraints on such effects of modified GW propagation. 5.2.5. Populations of Compact Binaries With a multitude of observed CBCs, one can infer the underlying population of these sources. In doing so, one needs to account for the detector selection effects, e.g., the fact that events that are farther away are less likely to be detected as compared to events that are nearby. One key element of the population that can be measured is the local merger rate density, R, representing the number of CBCs occurring per unit time per unit volume in the local Universe (E. S. Phinney 1991; C. Kim et al. 2003; P. R. Brady et al. 2004; R. Biswas et al. 2009; W. M. Farr et al. 2015; B. P. Abbott et al. 2016e), or its evolution with cosmic redshiftR z( ), which is the number of coalescences per unit source-frame time per unit comoving volume at a cosmological redshift of z (M. Fishbach et al. 2018). Another is the population distribution of masses and spins of merging compact binaries, p(m1, m2, S1, S2), which might also evolve over cosmic history, p(m1, m2, S1, S2|z). The measurement uncertainty in single-event parameters and the total number of detected events dictate the measurability of features in the population. These inferences are important in understanding the underlying astrophysical formation channels of compact binaries (e.g., S. Stevenson et al. 2017; W. M. Farr et al. 2017; M. Zevin et al. 2021; I. Mandel & F. S. Broekgaarden 2022). Inference of the Population of CBCs. In the companion article A. G. Abac et al. (2025c), we present measurements of the local rate of BNS, NSBH, and BBH mergers; inference of 29 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. the evolution of the CBC rate over cosmological time; and inference of the distribution of masses and spins of CBCs. 6. Synopsis This Letter serves as an introduction to the collection of articles accompanying the LVK’s GWTC-4.0. We have provided an overview of the GW detectors and observing runs of the LVK network and of the observed GWs from CBCs. The primary sequels to this introduction are a description of the methods used to perform searches for GWs in LVK data and to characterize source properties of identified signals (A. G. Abac et al. 2025a) and a summary of the main observations of GWTC-4.0, highlighting new CBC candidates and their estimated estimated masses and spins (A. G. Abac et al. 2025b). Other companion articles presenting science results from the analysis of the GWTC-4.0 candidates were described in Section 1. GWTC provides a prodigious census of over 200 merging BHs and NSs spanning two orders of magnitude in mass from ∼1M⊙ NSs to remnant BHs exceeding 100M⊙. Study of these observations will provide new insight into the nature of these objects, their population distribution, and their formation channels. These GW observations allow for sensitive tests of GR and provide information about the cosmological expansion history. Acknowledgments This material is based on work supported by NSF’s LIGO Laboratory, which is a major facility fully funded by the National Science Foundation. The authors also gratefully acknowledge the support of the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max- Planck-Society (MPS), and the State of Niedersachsen/ Germany for support of the construction of Advanced LIGO and construction and operation of the GEO 600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowl- edge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS), and the Netherlands Organization for Scientific Research (NWO) for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies, as well as by the Council of Scientific and Industrial Research of India; the Department of Science and Technology, India; the Science & Engineering Research Board (SERB), India; the Ministry of Human Resource Development, India; the Spanish Agencia Estatal de Investigación (AEI); the Spanish Ministerio de Ciencia, Innovación y Universidades; the European Union NextGener- ationEU/PRTR (PRTR-C17.I1); the ICSC—CentroNazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, funded by the European Union Next- GenerationEU; the Comunitat Autonòma de les Illes Balears through the Conselleria d’Educació i Universitats; the Con- selleria d’Innovació, Universitats, Ciència i Societat Digital de la Generalitat Valenciana and the CERCA Programme Generalitat de Catalunya, Spain; the Polish National Agency for Academic Exchange; the National Science Centre of Poland and the European Union—European Regional Devel- opment Fund; the Foundation for Polish Science (FNP); the Polish Ministry of Science and Higher Education; the Swiss National Science Foundation (SNSF); the Russian Science Foundation; the European Commission; the European Social Funds (ESF); the European Regional Development Funds (ERDF); the Royal Society; the Scottish Funding Council; the Scottish Universities Physics Alliance; the Hungarian Scien- tific Research Fund (OTKA); the French Lyon Institute of Origins (LIO); the Belgian Fonds de la Recherche Scientifique (FRS-FNRS), Actions de Recherche Concertées (ARC) and Fonds Wetenschappelijk Onderzoek—Vlaanderen (FWO), Belgium; the Paris Île-de-France Region; the National Research, Development and Innovation Office of Hungary (NKFIH); the National Research Foundation of Korea; the Natural Sciences and Engineering Research Council of Canada (NSERC); the Canadian Foundation for Innovation (CFI); the Brazilian Ministry of Science, Technology, and Innovations; the International Center for Theoretical Physics South American Institute for Fundamental Research (ICTP-SAIFR); the Research Grants Council of Hong Kong; the National Natural Science Foundation of China (NSFC); the Israel Science Foundation (ISF); the US–Israel Binational Science Fund (BSF); the Leverhulme Trust; the Research Corporation; the National Science and Technology Council (NSTC), Taiwan; the United States Department of Energy; and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, INFN, and CNRS for provision of computational resources. This work was supported by MEXT; the JSPS Leading-edge Research Infrastructure Program, JSPS Grant-in-Aid for Specially Promoted Research 26000005, JSPS Grant-in-Aid for Scientific Research on Innovative Areas 2402: 24103006, 24103005, and 2905: JP17H06358, JP17H06361, and JP17H06364, JSPS Core-to-Core Program A. Advanced Research Networks, JSPS Grants-in-Aid for Scientific Research (S) 17H06133 and 20H05639, JSPS Grant-in-Aid for Transformative Research Areas (A) 20A203: JP20H05854; the joint research program of the Institute for Cosmic Ray Research, University of Tokyo; the National Research Foundation (NRF); the Computing Infrastructure Project of the Global Science experimental Data hub Center (GSDC) at KISTI; the Korea Astronomy and Space Science Institute (KASI); the Ministry of Science and ICT (MSIT) in Korea; Academia Sinica (AS), the AS Grid Center (ASGC), and the National Science and Technology Council (NSTC) in Taiwan under grants including the Science Vanguard Research Program; the Advanced Technology Center (ATC) of NAOJ; and the Mechanical Engineering Center of KEK. Additional acknowledgments for support of individual authors may be found in the following document: https:// dcc.ligo.org/LIGO-M2300033/public. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manu- script version arising. We request that citations to this article use “A. G. Abac et al. (LIGO–Virgo–KAGRA Collaboration), ...” or similar phrasing, depending on journal convention. Facilities: EGO:Virgo, GEO600, Kamioka:KAGRA, LIGO. Software: Plots were prepared with MATPLOTLIB (J. D. Hunter 2007) and SEABORN (M. Waskom 2021). ASTROPY (A. M. Price-Whelan et al. 2022), GWPY (D. M. Macleod et al. 2021), LALSUITE (LIGO–Virgo– KAGRA Collaboration 2018; K. Wette 2020), NUMPY (C. R. Harris et al. 2020), and SCIPY (P. Virtanen et al. 2020) 30 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. https://dcc.ligo.org/LIGO-M2300033/public https://dcc.ligo.org/LIGO-M2300033/public were used for data processing in generating the figures and quantities in the manuscript. Data availability Event data used within this work are openly available in the GWTC-4.0 online catalog, which is hosted at https://gwosc. org/GWTC-4.0 and documented further in A. G. Abac et al. (2025i). Data behind Figures 1, 2, and 3 can be found in LIGO–Virgo–KAGRA Collaboration (2025). Appendix A Acronyms and Glossary This is a reference of frequently used terms and acronyms. A+: Advanced+ LIGO refers to a configuration of LIGO following a series of upgrades, some in advance of O4 (such as the addition of a new 300 m filter cavity for frequency-dependent vacuum squeezing), and some planned in advance of O5, such as installation of new optics with lower noise and loss (B. P. Abbott et al. 2020a; S. J. Cooper et al. 2023). A♯: LIGO A♯ (A-sharp) is a proposed upgrade of the Advanced+ LIGO interferometers anticipated on a post-O5 timeline. The baseline A♯ design is a room-temperature 1 μm laser wavelength inter- ferometer upgrade with larger test masses having coatings with lower thermal noise, higher laser power, and increased levels of vacuum squeezing (P. Fritschel et al. 2024). AdV: Advanced Virgo refers to an upgraded Virgo detector (F. Acernese et al. 2015) with an advanced interferometer. Virgo operated with the AdV configuration during O2 and O3. AdV+: Advanced Virgo+ is an upgrade to the AdV detector to take place in two phases: the first phase for operation during O4, and the second phase for operation during O5. aLIGO: Advanced LIGO refers to an upgraded LIGO configuration with advanced interferometers installed at both LHO and LLO. LIGO operated with the aLIGO configuration during O1, O2, O3, and O4 (J. Aasi et al. 2015a). BBH: Binary black hole. A binary system where both components are BHs. BH: Black hole. BHNS: Black hole–neutron star specifically refers to systems in which the BH formed before the NS. See also NSBH. bKAGRA: Baseline-design KAGRA is a configuration of the KAGRA detector as a cryogenic dual-recycled Fabry–Perot Michelson interferometer. bKAGRA phase-1 operation without power- or signal recy- cling took place from 2018 April 28 to 2018 May 6 2018 (T. Akutsu et al. 2019). BNS: Binary neutron star. A binary system where both components are NSs. CBC: Compact binary coalescence. The gravitational- radiation-driven orbital decay resulting in merger of a binary system made of two compact objects (NSs or BHs). CI: Credible interval. See CL. CL: Credible level. Given an n = 1 univariate or n- dimensional multivariate random variable x having probability density function (pdf) p(x) and an n- dimensional region R n, then the CL α of the region R n is the probability of x lying in R n, x xP R p d xn R n n( ) ( )= = . The region R n is then known as a 100α% CL credible region, with special cases: credible interval (CI) if n = 1, credible area if n = 2, or credible volume if n = 3. When n > 1, we normally take R n to be the region having the smallest volume that has CL α (the highest-density region). When n = 1 (CI), R1 is normally chosen to be an equal-tailed interval (also known as a symmetric interval), from the α/2 quantile to the 1 − α/2 quantile, but sometimes the smallest highest-density interval is used instead. EOS: Equation of state of an NS. For cold NSs (having temperature below the Fermi temperature), the EOS is of a barotropic fluid, a relationship between the energy density of the fluid and its pressure. FAR: False-alarm rate. Often used as a detection threshold, the probability of any one or more of a sequence of statistical tests performed over a duration T erroneously rejecting a null hypothesis is T1 exp FAR( )× . FAR therefore has dimen- sions of time−1. When interpreted as a measure of a detection significance of a candidate detection, this is the rate at which noise alone would produce more significant candidates. GEO: The GEO600 GW detector is a British–German �-shaped interferometric GW detector with 600m arms located near Hannover, Germany (B. Willke et al. 2002). GR: General relativity. Einstein’s theory of gravitation. GW: Gravitational wave. See Sections 1 and 5.1. GWOSC: The Gravitational Wave Open Science Center (for- merly known as the LIGO open science center) was created to provide public access to GW data products (R. Abbott et al. 2021d). The GWOSC online data and resources can be found at https://gwosc.org. GWTC: The Gravitational-Wave Transient Catalog is the electronic catalog of GW transients observed by LIGO, Virgo, and KAGRA detectors produced by the LVK. IFAR: Inverse false-alarm rate. The reciprocal of FAR, IFAR = (FAR)−1, having dimensions of time. A larger IFAR implies a more significant candidate, while a larger FAR implies a less significant candidate. IFO: Interferometer, a type of detector that uses laser interferometry to measure changes in the lengths of optical paths induced by GWs. IGWN: The International GW Observatory Network is a self-governing consortium using ground-based GW interferometers to explore the fundamental physics of gravity and to observe the Universe. The observatory network includes the KAGRA, LHO, LLO, and Virgo detectors. In addition, the GEO detector serves as a technology test bed and operates in an astrowatch mode outside of other detectors’ observing periods. 31 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. https://gwosc.org/GWTC-4.0 https://gwosc.org/GWTC-4.0 https://gwosc.org iKAGRA: Initial-phase KAGRA is a configuration of the KAGRA detector as a simple Michelson interfe- rometer that consists of two end test masses and a beam splitter. iKAGRA was operated from 2016 March 25 to 2016 March 31 and from 2016 April 11 to 2016 April 25 (T. Akutsu et al. 2018). IMBH: Intermediate-mass black hole. A BH in the mass range ∼102M⊙ to ∼105M⊙. KAGRA: KAGRA is a Japanese �-shaped interferometric GW detector with 3 km arms located underground at the Kamioka Observatory in Japan (T. Akutsu et al. 2021). KAGRA Collaboration: The KAGRA Collaboration manages the building, operation, and development of the KAGRA detector. LHO: The LIGO Hanford Observatory, one of the two LIGO observatories, located in Hanford, Washington, is an �-shaped interferometric GW detector with 4 km arms. LIGO: The Laser Interferometer Gravitational-Wave Obser- vatory consists of two widely spaced installations within the United States: one in Hanford, Washington (LHO), and the other in Livingston, Louisiana (LLO). LIGO is operated by the LIGO Laboratory, a consortium of the California Institute of Technology and the Massachusetts Institute of Technology funded by the US National Science Foundation. LLO: The LIGO Livingston Observatory, one of the two LIGO observatories, located in Livingston, Louisiana, is an �-shaped interferometric GW detector with 4 km arms. LSC: The LIGO Scientific Collaboration, founded in 1997, is a group of more than 1000 scientists that carries out science related to the LIGO detectors and their observations. LV: The LIGO–Virgo Collaboration. Prior to O3b, all observational results were published by the LV. LVC: The LIGO–Virgo Collaboration. The acronym LV is now preferred. LVK: The LIGO–Virgo–KAGRA Collaboration. NS: Neutron star. NSBH: The general term for a neutron star–black hole binary: a binary system in which one component is an NS and the other is a BH. If used in distinction with BHNS, it refers to such systems in which the NS formed before the BH. NR: Numerical relativity, the use of numerical methods to solve relativistic field equations. O1: The first observing run began on 2015 September 12 and ended on 2016 January 19. The LHO and LLO detectors participated in this observing run. O2: The second observing run began on 2016 November 30 and ended on 2016 August 25, during which the LHO and the LLO detectors were operating. On 2017 August 1, the AdV detector joined the observing run, forming a three-detector network. O3: The third observing run began on 2019 April 1 and ended on 2020 March 27, during which the LHO, LLO, and Virgo detectors were operating. A commissioning break from 2019 October 1 to 2019 November 1 divided O3 into two parts, O3a and O3b. A subsequent short run, O3GK, from 2020 April 7 to 2020 April 21 with GEO and KAGRA observing, followed O3b. O3a: The first, pre–commissioning break part of O3, from 2019 April 1 to October 1, during which the LHO, LLO, and Virgo detectors were operating. O3b: The second, post–commissioning break part of O3, from 2019 November 1 to 2020 March 27, during which the LHO, LLO, and Virgo detectors were operating. O3b was planned to continue until 2020 April 30 but ended early owing to the COVID-19 pandemic. O3GK: A short observing run after O3b from 2020 April 7 to 2020 April 21, during which the KAGRA and GEO detectors were observing. KAGRA had intended to join LIGO and Virgo at the end of O3, but the early end of O3b made this impossible. O4: The fourth observing run began on 2023 May 24 and is planned to continue into late 2025. It is divided into parts, the first of which, O4a, covered the period from 2023 May 24 until a commissioning break from 2024 January 16 to 2024 April 10. During O4a, LHO and LLO were observing. Following the break, observing continued in O4b from 2024 April 10 until an original intended end date of 2025 January 23, with LHO, LLO, and Virgo observing. It was decided to continue O4 observing in a third period O4c, beginning 2025 January 23 and lasting until 2025 November 18. O4a: The first part of the fourth observing run including data from 2023 May 24 until a commissioning break that began on 2024 January 16. During O4a, LHO and LLO were observing. O4b: The second part of the fourth observing run starting at the end of a commissioning break on 2024 April 10 and ending on the originally planned O4 end date of 2025 January 23. During O4b, LHO, LLO, and Virgo were observing. It was decided to continue O4 observations with a third part, O4c, immediately following the end of O4b on 2025 January 23. O4c: The third part of the fourth observing run, extending the run beyond its intended end date of 2025 January 23 through 2025 November 18. A commissioning break in O4c took place between 2025 April 1 and 2025 June 11. O5: The fifth observing run is the planned future observing run to follow O4. pdf: Probability density function. Given an n = 1 univariate or n-dimensional multivariate random variable x, the probability of x lying in an n-dimensional region Rn is x xP R p d xn R n n( ) ( )= , where p(x) is the pdf. PE: Parameter estimation, the process of measuring the parameters that describe the source of a signal, e.g., the masses and spins of the binary components of a CBC, from the observational data. PN: Post-Newtonian, a perturbative method of obtaining solutions to relativistic field equations based on slow- motion and weak-field expansion of the spacetime metric and the stress–energy source. PSD: Power spectral density. See Appendix B. SNR: Signal-to-noise ratio. See Appendix B. Virgo: The Virgo detector is a European �-shaped interfero- metric GW detector with 3 km arms located near Cascina, Italy (near Pisa). VirgoNEXT: Virgo_nEXT is a planned, post-O5, major upgrade of Virgo to fill the gap between the current phase, AdV+, and next-generation detectors. 32 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. Virgo Collaboration: The Virgo Collaboration manages the building, operation, and development of the Virgo detector. Appendix B Conventions for Data Analysis This appendix serves to define the data analysis conventions that will be used throughout the GWTC-4.0 companion articles. For a general introduction to data analysis we refer the reader to B. P. Abbott et al. (2020c) and references therein. Time series a(t) and frequency series a t˜( ) are related to each other by our conventions for the Fourier transform a f a t ift dtexp 2 23˜( ) ( ) ( ) ( )= + and its inverse transform a t a f ift dfexp 2 . 24( ) ˜( ) ( ) ( )= + + With these conventions, the dimensions of ã are a a time[ ˜] [ ]= × . Detector noise is often taken to be a stochastic Gaussian process. If n(t) is a real-valued stochastic Gaussian process, then the one-sided PSD Sn( f ) is formally defined by *n f n f S f f f 1 2 , 25n˜ ( ) ˜( ) ( ) ( ) ( )= where 〈 · 〉 is a statistical ensemble average of realizations of n(t) and *ñ is the complex conjugate of ñ. The one-sided PSD is defined only for f � 0. With these conventions, the dimensions of Sn are [Sn] = [n]2 × time. Real detector noise is neither entirely stationary nor Gaussian (B. P. Abbott et al. 2020c). However, it is often sufficient to assume that n(t) is ergodic such that S f T n t ift dtlim 2 exp 2 . 26n T T T 2 2 2 ( ) ( ) ( ) ( ) / / = The factor of two in the one-sided PSD ensures that the integrated power is S f df T n t dtlim 1 . 27n T T T 0 2 2 2( ) ( ) ( ) / / = The amplitude spectral density is defined to be the square root of the PSD, S fn 1 2( )/ . We often use a detector-noise-weighted inner product between two real-valued time series, a(t) and b(t), which is defined as * a b a f b f S f df4 Re 28a n0 ˜ ( ) ˜( ) ( ) ( )= + *a f b f S f df 1 2 , 28b n ˜ ( ) ˜( ) ( ) ( ) ( ) / = + where Sn( f ) is the detector’s one-sided PSD for the readout noise from that detector. The second form, Equation (28b), is an appropriate generalization of the inner product for complex- valued time series. Since GW detectors are insensitive at very low frequencies, the mean of the detector readout is arbitrary, and so we take the detector noise to have zero mean, 〈n(t)〉 = 0. Gaussian noise is then entirely characterized by its PSD, and its distribution is given by the probability density p n W n n 1 exp 1 2 , 29( ) ( )= where W is a usually neglected normalizing constant, the path integral DW n n nexp 2( )/= . Consider a template waveform u(t) that is unit normalized, 〈u|u〉 = 1, which is expected to match a hypothetical signal in detector data d(t). The matched filter SNR is u d . 30mf ( )= If data d(t) = n(t) + h(t) contain Gaussian noise n(t) plus a signal h(t) that is perfectly matched by the template waveform, h(t) ∝ u(t), then ρmf is a random variable having a normal distribution with unit variance and mean equal to the optimal SNR h h . 31opt ( )= The likelihood that detector data d(t) contains a signal h(t) is given by Equation (29) with n(t) = d(t) − h(t), p d h W d h d h 1 exp 1 2 32a( ) ( )= d d W h d h h exp 2 exp 1 2 32b ( ) ( )/ = p d exp 1 2 , 32cmf opt opt 2( ) ( )= where ρmf is the matched filter SNR with unit-normalized template u(t) ∝ h(t) and p d W d dexp 21( ) ( )/= is the likelihood under the no-signal hypothesis, d(t) = n(t). The likelihood is viewed as a functional of h(t) for a given realization of detector data d(t). The second factor in Equation (32c) is the signal-to-noise likelihood ratio p d h p d( ) ( )/ . Note that the likelihood ratio is a monotonically increasing function of the matched filter SNR, and so ρmf is the uniformly most powerful test for a known signal in Gaussian detector noise (J. Neyman & E. S. Pearson 1933). If the amplitude of the signal is unknown, h(t) = ρoptu(t) with unknown ρopt, then the likelihood is maximized for ρopt = ρmf and p d u p dmax exp 1 2 . 33opt mf 2 opt ( ) ( ) ( )= For the Newtonian inspiral of Section 5.2.1, the signal observed in a detector can be obtained in the frequency domain under the stationary phase approximation as (B. S. Sathyaprakash & S. V. Dhurandhar 1991; C. Cutler et al. 1993) M M M h f G c G c D G f c i f 5 24 exp , 34 3 2 eff 3 7 6 ˜( ) ( ( )) ( ) / = × where Ψ( f ) is the stationary phase function and D r F F , , 1 2 1 2 cos , , cos 35 eff 2 2 2 2 2 1 2 ( ) ( ) ( )/ = + + + × 33 The Astrophysical Journal Letters, 995:L18 (45pp), 2025 December 10 Abac et al. is the effective distance (B. Allen et al. 2012), which is related to the distance to the binary r by a factor that accounts for the orientation angles that describe the position of the source on the sky (ϑ, j), its inclination ι, and polarization angle ψ. Since F F 12 2++ × (with equality for a source on the zenith or nadir of an �-shaped interferometric detector), Deff� r (with equality only if ι = 0 or ι = π). The optimal SNR for such a signal is M MG c D G c f S f df 5 6 . 36 n opt 2 eff 3 1 6 0 7 3 ( ) ( ) / / = × + The horizon distance Dhor (B. Allen et al. 2012) of a source is the effective distance of a signal from such a source that has SNR ρopt equal to some detection threshold ρth. Such sources would not be expected to be detected beyond the horizon distance, but not all nearer sources will be detected either. The sensitive volume (L. S. Finn & D. F. Chernoff 1993; H.-Y. Chen et al. 2021) is a measure of the effective volume of space in which randomly isotropically oriented and homo- geneously distributed identical sources will produce signals in the detector with SNR ρopt greater than the threshold ρth, V r dr d d d d d d sin sin sin 37a 2 opt th ( )= > D0.086084 4 3 . 37bhor 3 ( )= × If the merger rate density is R, then the expected number of detections in time T is RVT . For a standard measure of detector sensitivity, a binary source of two 1.4M⊙ objects (M M M2 1.4 1.221 5/= × ) is considered and a threshold SNR of ρth = 8 is adopted (H.-Y. Chen et al. 2021). The sensitive volume is converted into an equivalent spherical radius as V = (4π/3)R3 to obtain the BNS range R = Dhor/2.26478, Equation (1). ORCID iDs A. G. Abacaa https://orcid.org/0000-0003-4786-2698 K. Ackleyaa https://orcid.org/0000-0002-8648-0767 S. Adhicaryaa https://orcid.org/0009-0004-2101-5428 N. Adhikariaa https://orcid.org/0000-0002-4559-8427 R. X. 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Overview 1.1. The GWTC Sources and Science 1.2. The Electronic Catalog: GWTC 1.2.1. The Catalog Naming Convention 1.2.2. Candidate Naming Conventions 1.3. Outline 2. The International GW Observatory Network 3. Observing Runs 3.1. O1: The First Observing Run 3.2. O2: The Second Observing Run 3.3. O3: The Third Observing Run 3.4. O4: The Fourth Observing Run 4. Observatory Evolution 4.1. LIGO Hanford and Livingston Observatories 4.1.1. O1 4.1.2. O2 4.1.3. O3 4.1.4. O4a 4.1.5. Beyond O4 4.2. Virgo Observatory 4.2.1. O2 4.2.2. O3 4.2.3. O4 4.3. KAGRA Observatory 4.3.1. O3GK 4.3.2. O4 4.4. GEO Observatory 4.4.1. Astrowatch 4.4.2. O3GK 5. Review of Observed Transient Sources 5.1. Gravitational Waves 5.1.1. Transient GW Signals 5.1.2. Gravitational Lensing of GWs 5.1.3. GW Polarization and Propagation in Alternative Theories of Gravity 5.2. Compact Binary Coalescence 5.2.1. Newtonian Inspiral 5.2.2. Post-Newtonian Inspiral and Other Effects 5.2.3. Compact Binary Merger and Ringdown 5.2.4. Redshift and Cosmological Effects 5.2.5. Populations of Compact Binaries 6. Synopsis Data availability Appendix A. Acronyms and Glossary Appendix B. Conventions for Data Analysis References